bluuebunny/crossref_metadata_2025 huggingface dataset:
Existence of unliftable modules
Authors: Jorgensen David
Published: July 2002

Let

(
Q
,

n

)

(Q,\operatorname {\mathfrak {n}})

be a commutative Noetherian local ring, and let

R
=
Q

/

(
x
)

R=Q/(x)

where

x
x

is a non-zerodivisor of

Q
Q

contained in

n

\operatorname {\mathfrak {n}}

. Then a finitely generated

R
R

-module

M
M

is said to lift to

Q
Q

if there exists a finitely generated

Q
Q

-module

M
′

M’

such that

x
x

is

M
′

M’

-regular and

M
≅

M
′

/

x

M
′

M \cong M’/xM’

. In this paper we give a general construction of finitely generated

R
R

-modules of finite projective dimension over

R
R

which fail to lift to

Q
Q

provided

x
∈

n

2

x \in \operatorname {\mathfrak {n}}^{2}

and the depth of

R
R

is at least 2.
The maximal ideal space of 𝐻^{∞}(𝔻) with respect to the Hadamard product
Authors: Render Hermann
Published: July 2002

It is shown that the space of all regular maximal ideals in the Banach algebra

H

∞

(

D

)

H^{\infty }(\mathbb {D} )

with respect to the Hadamard product is isomorphic to

N

0

.

\mathbb {N} _{0}.

The multiplicative functionals are exactly the evaluations at the

n
n

-th Taylor coefficient. It is a consequence that for a given function

f
(
z
)
=

∑

n
=
0

∞

a

n

z

n

f(z) =\sum _{n=0}^{\infty }a_{n} z^{n}

in

H

∞

(

D

)

H^{\infty }(\mathbb {D} )

and for a function

F
(
z
)

F(z)

holomorphic in a neighborhood

U
U

of

0
0

with

F
(
0
)
=
0

F(0) =0

and

a

n

∈
U

a_{n} \in U

for all

n
∈

N

0

n \in \mathbb {N}_{0}

the function

g
(
z
)
=

∑

n
=
0

∞

F
(

a

n

)

z

n

g(z) =\sum _{n=0}^{\infty }F(a_{n} ) z^{n}

is in

H

∞

(

D

)
.

H^{\infty }(\mathbb {D} ) .
Positive differentials, theta functions and 𝐻² Hardy kernels
Authors: Yamada Akira
Published: July 2002

Let

R
R

be a planar regular region whose Schottky double

R
^

\hat {R}

has genus

g
g

and set

T
^

0

=
{
z
∈

C

g

|

−
1

z
∈

R

g

}

\hat {T}_0=\{z\in \mathbb {C}^g|\sqrt {-1}\,z\in \mathbb {R}^g \}

. For fixed

a
∈
R

a\in R

we determine the range of the function
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper F left-parenthesis e right-parenthesis equals theta left-parenthesis a minus a overbar plus e right-parenthesis slash theta left-parenthesis e right-parenthesis left-parenthesis e element-of ModifyingAbove upper T With caret Subscript 0 Baseline right-parenthesis">

F
(
e
)
=
θ
(
a
−

a
¯

+
e
)

/

θ
(
e
)
(
e
∈

T
^

0

)

F(e)=\theta (a-\bar {a}+e)/\theta (e) (e\in \hat {T}_0)

where

θ
(
z
)

\theta (z)

is the Riemann theta function on

R
^

\hat {R}

. Also we introduce two weighted Hardy spaces to study the problem when the matrix

(

∂
2

log
⁡
F

∂

z
i

∂

z
j

(
e
)
)

(\frac {\partial ^2\log F}{\partial z_i\partial z_j}(e))

is positive definite. The proof relies on new theta identities using Fay’s trisecants formula.
On a question in the theory of almost periodic differential equations
Authors: Hu Zuo , Mingarelli Angelo
Published: July 2002

We show that there exists a real homogeneous differential equation of order

n
n

with classical almost periodic coefficients such that all solutions are uniformly bounded on the real line yet no non-trivial solution is almost periodic. This now appears to make the search for a Floquet theory of such equations a futile enterprise.
One-to-one Borel selection theorems
Authors: Balcerzak Marek , Peredko Joanna
Published: July 2002

For

X
=
[
0
,
1
]

X=[0,1]

we obtain new theorems stating that a Borel set in

X
2

X^2

with large sets of large vertical and large horizontal sections admits a one-to-one Borel selection with large domain and large range. Largeness is meant mainly in measure or category sense. Our proofs combine a result of Graf and Mauldin with a modified result of Sarbadhikari.
Opial’s modulus and fixed points of semigroups of mappings
Authors: Kuczumow Tadeusz
Published: July 2002

If

X
X

is a Banach space with the non-strict Opial property and

r

X

(
1
)

>
0

r_{X}\left ( 1\right ) >0

and

C
C

is a nonempty convex weakly compact subset of

X
X

, then every semigroup

T

=

{

T

t

:
t
∈
G
}

\mathfrak {T}=\left \{ T_{t}:t\in G\right \}

of asymptotically regular selfmappings of

C
C

with

σ

(

T

)

>
1
+

r

X

(
1
)

\sigma \left ( \mathfrak {T}\right ) >1+r_{X}\left ( 1\right )

has a common fixed point.
Topological density of ccc Boolean algebras–Every cardinality occurs
Authors: Rabus Mariusz , Shelah Saharon
Published: July 2002

For every uncountable cardinal

μ
\mu

there is a ccc Boolean algebra whose topological density is

μ
\mu

.
Relative modular theory for a weight
Authors: Izumi Hideaki
Published: July 2002

We consider the balanced weight

χ
\chi

of a semi-finite weight

φ
\varphi

and a (not necessarily faithful) normal positive functional

ψ
\psi

on a von Neumann algebra

M

\mathcal M

, and discuss how the modular operator

Δ
χ

\Delta _\chi

and the modular conjugation

J
χ

J_\chi

are described under the identification of the standard Hilbert space

H

χ

\mathcal {H}_\chi

with

H

φ

⊕
p

H

φ

⊕

p
′

H

φ

⊕
p

p
′

H

φ

\mathcal {H}_\varphi \oplus p\mathcal {H}_\varphi \oplus p’\mathcal {H}_\varphi \oplus pp’\mathcal {H}_\varphi

, where

p
p

is the support projection of

ψ
\psi

and

p
′

=

J
φ

p

J
φ

∈

M

′

p’=J_\varphi p J_\varphi \in \mathcal {M}’

.
Serre’s condition 𝑅_{𝑘} for associated graded rings
Authors: Johnson Mark , Ulrich Bernd
Published: July 2002

A criterion is given for when the associated graded ring of an ideal satisfies Serre’s condition

R

k

R_{k}

. As an application, the integrality and quasi-Gorensteinness of such rings is investigated.
Pseudodifferential calculus on manifolds with corners and groupoids
Authors: Monthubert Bertrand
Published: July 2002

We build a longitudinally smooth, differentiable groupoid associated to any manifold with corners. The pseudodifferential calculus on this groupoid coincides with the pseudodifferential calculus of Melrose (also called

b
b

-calculus). We also define an algebra of rapidly decreasing functions on this groupoid; it contains the kernels of the smoothing operators of the (small)

b
b

-calculus.
Denjoy’s theorem with exponents
Authors: Norton Alec
Published: July 2002

If

X
X

is the (unique) minimal set for a

C

1
+
α

C^{1+\alpha }

diffeomorphism of the circle without periodic orbits,

0
>
α
>
1

0>\alpha >1

, then the upper box dimension of

X
X

is at least

α
\alpha

. The method of proof is to introduce the exponent

α
\alpha

into the proof of Denjoy’s theorem.
A non-metrizable compact linearly ordered topological space, every subspace of which has a 𝜎-minimal base
Authors: Shi Wei-Xue
Published: July 2002

A collection

D

\mathcal {D}

of subsets of a space is minimal if each element of

D

\mathcal {D}

contains a point which is not contained in any other element of

D

\mathcal {D}

. A base of a topological space is

σ
\sigma

-minimal if it can be written as a union of countably many minimal collections. We will construct a compact linearly ordered space

X
X

satisfying that

X
X

is not metrizable and every subspace of

X
X

has a

σ
\sigma

-minimal base for its relative topology. This answers a problem of Bennett and Lutzer in the negative.
Automatic extensions of local regularized semigroups and local regularized cosine functions
Authors: Wang Sheng , Gao Ming
Published: July 2002

This paper establishes automatic extensions for local regularized semigroups and local regularized cosine functions in a certain sense and applies the results to abstract Cauchy problems.
Large components of principal series and characteristic cycles
Authors: Chang Jen-Tseh
Published: July 2002

For a semisimple quasi-split real linear group which is also maximal in Kostant’s sense, a theorem of Vogan asserts that there is a unique composition factor that is large in any principal series. We give a proof of this theorem using results of Schmid and Vilonen that establish a conjecture of Barbasch and Vogan about characteristic cycles. As a byproduct, we obtain some information about the characteristic cycles of the localized

K
K

-equivariant sheaves of these principal series.
Volume, surface area and inward injectivity radius
Authors: Innami Nobuhiro
Published: July 2002

We show some relations among the volumes of domains in Euclidean spaces, their surface areas and the inward injectivity radii from their boundaries. In particular, we give an estimate for the upper bound of the ratios of their surface areas and volumes by means of inward injectivity radii. The upper bound seems to depend on their topological structures.
Random fluctuations of convex domains and lattice points
Authors: Iosevich Alex , Kinateder Kimberly
Published: July 2002

In this paper, we examine a random version of the lattice point problem. LetH\mathcal Hdenote the class of all homogeneous functions inC2(Rn)C^2(\mathbb R^n)of degree one, positive away from the origin. LetΦ\Phibe a random element ofH\mathcal H, defined on probability space(Ω,F,P)(\Omega ,\mathcal F,P), and define\[<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper F Subscript normal upper Phi left-parenthesis omega comma dot right-parenthesis Baseline left-parenthesis xi right-parenthesis equals integral Underscript StartSet x colon normal upper Phi left-parenthesis omega comma x right-parenthesis less-than-or-equal-to 1 EndSet Endscripts e Superscript minus i mathematical left-angle x comma xi mathematical right-angle Baseline d x">FΦ(ω,⋅)(ξ)=∫{x:Φ(ω,x)≤1}e−i⟨x,ξ⟩dxF_{\Phi (\omega ,\cdot )}(\xi )=\int _{\{x\colon \Phi (\omega ,x)\le 1\}}e^{-i\langle x,\xi \rangle }dx\]forω∈Ω\omega \in \Omega. We prove that, if<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper E left-parenthesis StartAbsoluteValue upper F Subscript normal upper Phi Baseline left-parenthesis xi right-parenthesis EndAbsoluteValue right-parenthesis less-than-or-equal-to upper C left-bracket xi right-bracket Superscript StartFraction n plus 1 Over 2 EndFraction">E(|FΦ(ξ)|)≤C[ξ]n+12E(|F_\Phi (\xi )|)\le C[\xi ]^{\frac {n+1}{2}}, where[ξ]=1+|ξ|[\xi ]=1+|\xi |, then\[<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper E left-parenthesis upper N Subscript normal upper Phi Baseline right-parenthesis left-parenthesis t right-parenthesis equals upper V t Superscript n Baseline plus upper O left-parenthesis t Superscript n minus 2 plus StartFraction 2 Over n plus 1 EndFraction Baseline right-parenthesis">E(NΦ)(t)=Vtn+O(tn−2+2n+1)E(N_\Phi )(t)=Vt^n+O(t^{n-2+\frac {2}{n+1}})\]whereV=E(|{x:Φ(⋅,x)≤1}|)V=E(|\{x\colon \Phi (\cdot ,x)\le 1\}|), the expected volume. That is, on average,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper N Subscript normal upper Phi Baseline left-parenthesis t right-parenthesis equals upper V t Superscript n Baseline plus upper O left-parenthesis t Superscript n minus 2 plus StartFraction 2 Over n plus 1 EndFraction Baseline right-parenthesis">NΦ(t)=Vtn+O(tn−2+2n+1)N_\Phi (t)=Vt^n+O(t^{n-2+\frac {2}{n+1}}). We give explicit examples in which the Gaussian curvature of{x:Φ(ω,x)≤1}\{x\colon \Phi (\omega ,x)\le 1\}is small with high probability, and the estimate<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper N Subscript normal upper Phi Baseline left-parenthesis t right-parenthesis equals upper V t Superscript n Baseline plus upper O left-parenthesis t Superscript n minus 2 plus StartFraction 2 Over n plus 1 EndFraction Baseline right-parenthesis">NΦ(t)=Vtn+O(tn−2+2n+1)N_\Phi (t)=Vt^n+O(t^{n-2+\frac {2}{n+1}})holds nevertheless.
Distributivity and stationary reflections
Authors: Kanai Yasuo
Published: July 2002

In this paper, we present some relations between generalized distributivity of quotient algebras and Mahlo operations, and show that the distributivity implies some variants of stationary relections.
Singular sets and maximal topologies
Authors: Kennedy G. , McCartan S.
Published: July 2002

Spaces which are maximal with respect to a semi-regular property are characterised. Furthermore, a method to construct such topologies is given. Consequently, new characterisations of maximal pseudocompact spaces and of maximal Q.H.C. spaces are presented. Known characterisations of maximal connected spaces and of maximal feebly compact spaces are given alternative proofs.
On pointwise convergence of Fourier series of radial functions in several variables
Authors: Kuratsubo Shigehiko
Published: July 2002

We prove the pointwise convergence of the Fourier series for radial functions in several variables, which in the case

n
=
1

n=1

is the Dirichlet-Jordan theorem itself. In our proof the method for the case of the indicator function of the ball is very useful.
A note on rigidity of 3-Sasakian manifolds
Authors: Pedersen Henrik , Poon Yat
Published: July 2002

Making use of the relations among 3-Sasakian manifolds, hypercomplex manifolds and quaternionic Kähler orbifolds, we prove that complete 3-Sasakian manifolds are rigid.
Regularity of CR maps between convex hypersurfaces of finite type
Authors: Coupet Bernard , Gaussier Hervé , Sukhov Alexandre
Published: July 2002

We study rigidity and regularity properties of CR maps between smooth convex hypersurfaces of finite type in

C

n
+
1

.

\mathbb C^{n+1}.
Injective factorization of holomorphic mappings
Authors: González Manuel , Gutiérrez Joaquín
Published: July 2002

We characterize the holomorphic mappings

f
f

between complex Banach spaces that may be written in the form

f
=
g
∘
T

f=g\circ T

, where

g
g

is another holomorphic mapping and

T
T

is an operator belonging to a closed injective operator ideal. Analogous results are previously obtained for multilinear mappings and polynomials.
Noetherian down-up algebras
Authors: Kirkman Ellen , Musson Ian , Passman D.
Published: July 2002

Down-up algebras

A
=
A
(
α
,
β
,
γ
)

A= A(\alpha ,\beta ,\gamma )

were introduced by G. Benkart and T. Roby to better understand the structure of certain posets. In this paper, we prove that

β
≠
0

\beta \neq 0

is equivalent to

A
A

being right (or left) Noetherian, and also to

A
A

being a domain. Furthermore, when this occurs, we show that

A
A

is Auslander-regular and has global dimension 3.
Spectrum preserving linear mappings for scattered Jordan-Banach algebras
Authors: Maouche Abdelaziz
Published: July 2002

Given two semisimple complex Jordan-Banach algebras with identity

A
A

and

B
B

, we say that

T
T

is a spectrum preserving linear mapping from

A
A

to

B
B

if

T
T

is surjective and we have

Sp
⁡
(
T
x
)
=
Sp
⁡
(
x
)

\operatorname {Sp}(Tx)=\operatorname {Sp}(x)

, for all

x
∈
A

x\in A

. We prove that if

B
B

is a scattered Jordan-Banach algebra, then

T
T

is a Jordan isomorphism.
Dimension of a minimal nilpotent orbit
Authors: Wang Weiqiang
Published: July 2002

We show that the dimension of the minimal nilpotent coadjoint orbit for a complex simple Lie algebra is equal to twice the dual Coxeter number minus two.
Matrix presentations of braids and applications
Authors: Lee Sang
Published: July 2002

We show that there exists a one-to-one correspondence between the class of certain block tridiagonal matrices with the entries

−
1
,
0
,

-1, 0,

or

1
1

and the free monoid generated by

2
n

2n

generators

σ

1

,
⋯
,

σ

n

,

σ

1

−
1

,
⋯
,

σ

n

−
1

\sigma _{1}, \cdots ,\sigma _{n}, \sigma _{1}^{-1},\cdots , \sigma _{n}^{-1}

and relation
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="sigma Subscript i Superscript plus-or-minus 1 Baseline sigma Subscript j Superscript plus-or-minus 1 Baseline equals sigma Subscript j Superscript plus-or-minus 1 Baseline sigma Subscript i Superscript plus-or-minus 1 Baseline left-parenthesis StartAbsoluteValue i minus j EndAbsoluteValue greater-than-or-equal-to 2 right-parenthesis">

σ

i

±
1

σ

j

±
1

=

σ

j

±
1

σ

i

±
1

 
(

|

i
−
j

|

≥
2
)

\sigma _{i}^{\pm 1}\sigma _{j}^{\pm 1} = \sigma _{j}^{\pm 1}\sigma _{i}^{\pm 1}~ (|i-j| \geq 2)

and give some applications for braids. In particular, we give new formulation of the reduced Alexander matrices for closed braids.
Generating sets for compact semisimple Lie groups
Authors: Field Michael
Published: July 2002

Let

Γ
\Gamma

be a compact connected semisimple Lie group. We prove that the subset of

Γ
2

\Gamma ^2

consisting of pairs

(
g
,
h
)

(g, h)

which topologically generate

Γ
\Gamma

is Zariski open.
Growth and covering theorems associated with the Roper-Suffridge extension operator
Authors: Graham Ian
Published: July 2002

The Roper-Suffridge extension operator, originally introduced in the context of convex functions, provides a way of extending a (locally) univalent function

f
∈
Hol
⁡
(

D

,

C

)

f\in \operatorname {Hol}(\mathbb {D},\mathbb {C})

to a (locally) univalent map

F
∈
Hol
⁡
(

B

n

,

C

n

)

F\in \operatorname {Hol}(B_{n},\mathbb {C}^{n})

. If

f
f

belongs to a class of univalent functions which satisfy a growth theorem and a distortion theorem, we show that

F
F

satisfies a growth theorem and consequently a covering theorem. We also obtain covering theorems of Bloch type: If

f
f

is convex, then the image of

F
F

(which, as shown by Roper and Suffridge, is convex) contains a ball of radius

π

/

4

\pi /4

. If

f
∈
S

f\in S

, the image of

F
F

contains a ball of radius

1

/

2

1/2

.
On groups with commutators of bounded order
Authors: Shumyatsky Pavel
Published: July 2002

Let

p
p

be a prime,

k
k

a non-negative integer. We prove that if

G
G

is a residually finite group such that

[
x
,
y

]

p
k

=
1

[x,y]^{p^k}=1

for all

x
,
y
∈
G

x,y\in G

, then

G
′

G’

is locally finite.
On the norm of the product of linear functionals
Authors: Benítez C. , Fernández Manuel , Soriano María
Published: July 2002

Real inner product spaces are characterized by the points at which the homogeneous 2-polynomials that are products of equal-norm linear functionals attain their norm.
On the multiplicity of eigenvalues of a vectorial Sturm-Liouville differential equation and some related spectral problems
Authors: Shen Chao-Liang , Shieh Chung-Tsun
Published: July 2002

We prove that under certain conditions, a vectorial Sturm- Liouville differential equation of dimension

n
≥
2

n \geq 2

can only possess finitely many eigenvalues which have multiplicity

n
n

. For the case

n
=
2

n=2

, we find a sufficient condition on the potential function

Q
(
x
)

Q(x)

, and a bound

m
Q

m_Q

depending on

Q
(
x
)

Q(x)

, such that the eigenvalues of the equation with index exceeding

m
Q

m_Q

are all simple. These results are applied to find some sufficient conditions which imply that the spectra of two potential equations, or two string equations, have finitely many elements in common, and an estimate of the number of elements in the intersection of two spectra is provided.
On automatic continuity of homomorphisms
Authors: Beddaa A. , Bhatt S. , Oudadess M.
Published: July 2002

Introducing a weaker notion of regularity in a topological algebra, we examine and improve an automatic continuity theorem given by the second author. Examples and applications are given.
On the Gelfand-Kirillov conjecture for quantum algebras
Authors: Caldero Philippe
Published: July 2002

Let

q
q

be a complex not a root of unity and

g

\mathfrak {g}

be a semi-simple Lie

C

\mathbb {C}

-algebra. Let

U

q

(

g

)

U_{q}(\mathfrak {g})

be the quantized enveloping algebra of Drinfeld and Jimbo,

U

q

(

n

−

)
⊗

U

0

⊗

U

q

(

n

)

U_{q}(\mathfrak {n}^-)\otimes U^{0}\otimes U_{q}(\mathfrak {n})

be its triangular decomposition, and

C

q

[
G
]

\mathbb {C}_{q}[G]

the associated quantum group. We describe explicitly

Fract
⁡

U

q

(

n

)

\operatorname {Fract} U_{q}(\mathfrak {n})

and

Fract
⁡

C

q

[
G
]

\operatorname {Fract}\mathbb {C}_{q}[G]

as a quantum Weyl field. We use for this a quantum analogue of the Taylor lemma.
A free analogue of Hincin’s characterization of infinite divisibility
Authors: Bercovici Hari , Pata Vittorino
Published: July 2002

Hinčin characterized the class of infinitely divisible distributions on the line as the class of all distributional limits of sums of infinitesimal independent random variables. We show that an analogue of this characterization is true in the addition theory of free random variables introduced by Voiculescu.
Bounded composition operators with closed range on the Dirichlet space
Authors: Luecking Daniel
Published: July 2002

For composition operators on spaces of analytic functions it is well known that norm estimates can be converted to Carleson measure estimates. The boundedness of the composition operator becomes equivalent to a Carleson measure inequality. The measure corresponding to a composition operator

C
φ

C_\varphi

on the Dirichet space

D

\mathcal D

is

d

ν
φ

=

n
φ

d
A

d\nu _\varphi = n_\varphi \,dA

, where

n
φ

(
z
)

n_\varphi (z)

is the cardinality of the preimage

φ

−
1

(
z
)

\varphi ^{-1}(z)

. The composition operator will have closed range if and only if the corresponding measure satisfies a “reverse Carleson measure” theorem:

‖
f

‖

D

2

≤
∫

|

f
′

|

2

d

ν
φ

\| f \|_{\mathcal {D}}^2 \le \int |f’|^2 \,d\nu _\varphi

for all

f
∈

D

f\in \mathcal D

. Assuming

C
φ

C_\varphi

is bounded, a necessary condition for this inequality is a reverse of the Carleson condition: (C) 

ν
φ

(
S
)
≥
c

|

S

|

\nu _\varphi (S) \ge c |S|

for all Carleson squares

S
S

. It has long been known that this is not sufficient for a completely general measure. Here we show that it is also not sufficient for the special measures

ν
φ

\nu _\varphi

. That is, we construct a function

φ
\varphi

such that

C
φ

C_\varphi

is bounded and

ν
φ

\nu _\varphi

satisfies (C) but the composition operator

C
φ

C_\varphi

does not have closed range.
Groups acting transitively on compact CR manifolds of hypersurface type
Authors: Spiro Andrea
Published: July 2002

Let

M
=
G

/

L

M=G/L

be a compact homogeneous manifold with

G
G

acting effectively and with a

G
G

-invariant CR structure of hypersurface type; then any maximal compact subgroup

K
⊂
G

K\subset G

acts transitively on

M
M

.
Codimension 2 nonfibrators with finite fundamental groups
Authors: Daverman R.
Published: July 2002

Fibrators are

n
n

-manifolds which automatically induce approximate fibrations, in the following sense: given any proper mapping

p
p

from an

(
n
+
k
)

(n+k)

-manifold onto a finite-dimensional metric space such that, up to shape, each point-preimage is a copy of the fibrator,

p
p

is necessarily an approximate fibration. This paper sets forth new examples, for the case

k
=
2

k=2

, of nonfibrators whose fundamental groups are finite.
Bousfield localizations of classifying spaces of nilpotent groups
Authors: Dwyer William , Dror Farjoun Emmanuel , Ravenel Douglas
Published: July 2002

Let

G
G

be a finitely generated nilpotent group. The object of this paper is to identify the Bousfield localization

L
h

B
G

L_hBG

of the classifying space

B
G

BG

with respect to a multiplicative complex oriented homology theory

h

∗

h_{*}

. We show that

L
h

B
G

L_hBG

is the same as the localization of

B
G

BG

with respect to the ordinary homology theory determined by the ring

h
0

h_0

.
Finite generation of powers of ideals
Authors: Gilmer Robert , Heinzer William , Roitman Moshe
Published: July 2002

Suppose

M
M

is a maximal ideal of a commutative integral domain

R
R

and that some power

M
n

M^n

of

M
M

is finitely generated. We show that

M
M

is finitely generated in each of the following cases: (i)

M
M

is of height one, (ii)

R
R

is integrally closed and

ht
⁡
M
=
2

\operatorname {ht} M=2

, (iii)

R
=
K
[
X
;

S
~

]

R = K[X;\tilde S]

is a monoid domain over a field

K
K

, where

S
~

=
S
∪
{
0
}

\tilde S = S \cup \{0\}

is a cancellative torsion-free monoid such that

⋂

m
=
1

∞

m
S
=
∅

\bigcap _{m=1}^\infty mS=\emptyset

, and

M
M

is the maximal ideal

(

X
s

:
s
∈
S
)

(X^s:s\in S)

. We extend the above results to ideals

I
I

of a reduced ring

R
R

such that

R

/

I

R/I

is Noetherian. We prove that a reduced ring

R
R

is Noetherian if each prime ideal of

R
R

has a power that is finitely generated. For each

d
d

with

3
≤
d
≤
∞

3 \le d \le \infty

, we establish existence of a

d
d

-dimensional integral domain having a nonfinitely generated maximal ideal

M
M

of height

d
d

such that

M
2

M^2

is

3
3

-generated.
Calculating and interpreting the Mislin genus of a special class of nilpotent spaces
Authors: Hilton Peter , Scevenels Dirk
Published: July 2002

We prove that there is a bijection between the Mislin genus of a circle bundle over a certain nilpotent base space

M
M

, which is constructed from a nilpotent group

N
N

of a certain specified type, and the Mislin genus of

N
N

itself.
A characterization of Möbius transformations
Authors: Höfer Roland
Published: July 2002

Let

n
≥
2

n\ge 2

be an integer and let

D

\mathcal {D}

be a domain of

R

n

\mathbb {R}^n

. Let

f
:

D

→

R

n

f:\mathcal {D}\to \mathbb {R}^n

be an injective mapping which takes hyperspheres whose interior is contained in

D

\mathcal {D}

to hyperspheres in

R

n

\mathbb {R}^n

. Then

f
f

is the restriction of a Möbius transformation.
The mod 2 homology of BSO
Authors: Rodrigues Claudina
Published: July 2002

This note is about a set of generators to the mod 2 homology of BSO.
On 𝐾-contact manifolds with minimal number of closed characteristics
Authors: Rukimbira Philippe
Published: July 2002

We prove that closed simply connected K-contact manifolds with minimal number of closed characteristics are homeomorphic to odd-dimensional spheres.
Tilting up iterated tilted algebras
Authors: Assem Ibrahim , Happel Dieter , Trepode Sonia
Published: July 2002

We show that, if

A
A

is a representation-finite iterated tilted algebra of euclidean type

Q
Q

, then there exist a sequence of algebras

A
=

A

0

,

A

1

,

A

2

,
…
,

A

m

A=A_{0},A_{1},A_{2},\dots , A_{m}

, and a sequence of modules

T

A

i

(
i
)

T^{(i)}_{A_{i}}

, where

0
≤
i
>
m

0\leq i>m

, such that each

T

A

i

(
i
)

T^{(i)}_{A_{i}}

is an APR-tilting

A

i

A_{i}

-module, or an APR-cotilting

A

i

A_{i}

-module,

End
⁡

T

A

i

(
i
)

=

A

i
+
1

\operatorname {End} T^{(i)}_{A_{i}}=A_{i+1}

and

A

m

A_{m}

is tilted representation-finite.
Hilbert space idempotents and involutions
Authors: Buckholtz Don
Published: July 2002

Norms of idempotents, involutions, and the Hermitian and skew-Hermitian parts of involutions are shown to be elementary trigonometric functions of an angle between two subspaces of Hilbert space. When the spaces involved are nontrivial, the norm of a linear idempotent is the cosecant of the angle between its range and kernel; the norm of a linear involution is the cotangent of half the angle between the involution’s eigenspaces.
Weighted Caccioppoli-type estimates and weak reverse Hölder inequalities for 𝐴-harmonic tensors
Authors: Ding Shusen
Published: July 2002

We obtain a local weighted Caccioppoli-type estimate and prove the weighted version of the weak reverse Hölder inequality for

A
A

-harmonic tensors.
Collapsibility of Δ(Π_{𝑛})/𝒮_{𝓃} and some related CW complexes
Authors: Kozlov Dmitry
Published: July 2002

Let

Δ
(

Π
n

)

\Delta (\Pi _n)

denote the order complex of the partition lattice. The natural

S

n

\mathcal {S}_n

-action on the set

[
n
]

[n]

induces an

S

n

\mathcal {S}_n

-action on

Δ
(

Π
n

)

\Delta (\Pi _n)

. We show that the regular CW complex

Δ
(

Π
n

)

/

S

n

\Delta (\Pi _n)/\mathcal {S}_n

is collapsible. Even more, we show that

Δ
(

Π
n

)

/

S

n

\Delta (\Pi _n)/\mathcal {S}_n

is collapsible, where

Π
Δ

\Pi _\Delta

is a suitable type selection of the partition lattice. This allows us to generalize and reprove in a conceptual way several previous results regarding the multiplicity of the trivial character in the

S

n

\mathcal {S}_n

-representation on

H
∗

(
Δ
(

Π
n

)
)

H_*(\Delta (\Pi _n))

.
An extension of multi-valued contraction mappings and fixed points
Authors: Zhong Cheng-Kui , Zhu Jiang , Zhao Pei-Hao
Published: July 2002

A class of new multi-valued contraction mappings is presented. Under the new contractive conditions, some fixed point theorems for multi-valued self-mappings and nonself-mappings are proved.
The 𝐶*-algebras of infinite graphs
Authors: Fowler Neal , Laca Marcelo , Raeburn Iain
Published: July 2002

We associate

C
∗

C^*

-algebras to infinite directed graphs that are not necessarily locally finite. By realizing these algebras as Cuntz-Krieger algebras in the sense of Exel and Laca, we are able to give criteria for their uniqueness and simplicity, generalizing results of Kumjian, Pask, Raeburn, and Renault for locally finite directed graphs.
A bound on the reduction number of a primary ideal
Authors: Rossi M.
Published: July 2002

Let

(
A
,

M

)

( A,\mathcal {M})

be a local ring of positive dimension

d
d

and let

I
I

be an

M

\mathcal {M}

-primary ideal. We denote the reduction number of

I
I

by

r
(
I
)

r(I)

, which is the smallest integer

r
r

such that

I

r
+
1

=
J

I
r

I^{r+1}=JI^r

for some reduction

J
J

of

I
.

I.

In this paper we give an upper bound on

r
(
I
)

r(I)

in terms of numerical invariants which are related with the Hilbert coefficients of

I
I

when

A
A

is Cohen-Macaulay. If

d
=
1

d=1

, it is known that

r
(
I
)
≤
e
(
I
)
−
1

r(I) \le e(I) -1

where

e
(
I
)

e(I)

denotes the multiplicity of

I
.

I.

If

d
≤
2
,

d \le 2,

in Corollary 1.5 we prove
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="r left-parenthesis upper I right-parenthesis less-than-or-equal-to e 1 left-parenthesis upper I right-parenthesis minus e left-parenthesis upper I right-parenthesis plus lamda left-parenthesis upper A slash upper I right-parenthesis plus 1">

r
(
I
)
≤

e
1

(
I
)
−
e
(
I
)
+
λ
(
A

/

I
)
+
1

r(I) \le e_1(I) - e(I) + \lambda (A/I) + 1

where

e
1

(
I
)

e_1(I)

is the first Hilbert coefficient of

I
.

I.

From this bound several results follow. Theorem 1.3 gives an upper bound on

r
(
I
)

r(I)

in a more general setting.
A lower bound for the number of components of the moduli schemes of stable rank 2 vector bundles on projective 3-folds
Authors: Ballico E. , Miró-Roig R.
Published: July 2002

Fix a smooth projective 3-fold

X
X

,

c
1

c_1

,

H
∈

P
i
c

(
X
)

H\in \mathrm {Pic}(X)

with

H
H

ample, and

d
∈

Z

d\in \mathbf {Z}

. Assume the existence of integers

a
,
b

a,b

with

a
≠
0

a\not =0

such that

a

c
1

ac_1

is numerically equivalent to

b
H

bH

. Let

M
(
X
,
2
,

c
1

,
d
,
H
)

M(X,2,c_1,d,H)

be the moduli scheme of

H
H

-stable rank 2 vector bundles,

E
E

, on

X
X

with

c
1

(
E
)
=

c
1

c_1(E)=c_1

and

c
2

(
E
)
⋅
H
=
d

c_2(E)\cdot H=d

. Let

m
(
X
,
2
,

c
1

,
d
,
H
)

m(X,2,c_1,d,H)

be the number of its irreducible components. Then

lim sup

d
→
∞

m
(
X
,
2
,

c
1

,
d
,
H
)
=
+
∞

\limsup _{d\rightarrow \infty }m(X,2,c_1,d,H)= +\infty

.
Approximation for bootstrapped empirical processes
Authors: Csörgő Miklós , Horváth Lajos , Kokoszka Piotr
Published: July 2002

We obtain an approximation for the bootstrapped empirical process with the rate of the Komlós, Major and Tusnády approximation for empirical processes. The proof of the new approximation is based on the Poisson approximation for the uniform empirical distribution function and the Gaussian approximation for randomly stopped sums.
Uniform bounds for stably integral points on elliptic curves
Authors: Pacelli Patricia
Published: July 2002

We show that a conjecture by Lang and Vojta regarding integral points on varieties of logarithmic general type implies the existence of a uniform bound on the number of stably

S
S

-integral points on an elliptic curve over a degree-

d
d

number field.
Unions of John domains
Authors: Väisälä Jussi
Published: July 2002

We study the question: When is the union of John domains a John domain?
Algebraic gamma monomials and double coverings of cyclotomic fields
Authors: Das Pinaki
Published: July 2002

We investigate the properties of algebraic gamma monomials—that is, algebraic numbers which are expressible as monomials in special values of the classical gamma function. Recently Anderson has constructed a double complex

S
K

{\mathbb {SK}}

, to compute

H
∗

(
±
,

U

)

H^*(\pm , {\mathbb {U}})

, where

U

{\mathbb {U}}

is the universal ordinary distribution. We use the double complex to deduce explicit formulae for algebraic gamma monomials. We provide simple proofs of some previously known results of Deligne on algebraic gamma monomials. Deligne used the theory of Hodge cycles for his results. By contrast, our proofs are constructive and relatively elementary. Given a Galois extension

K

/

F

K/F

, we define a double covering of

K

/

F

K/F

to be an extension

K
~

/

K

\tilde {K}/K

of degree

≤
2

\leq 2

, such that

K
~

/

F

{\tilde {K}}/F

is Galois. We demonstrate that each class

a

∈

H
2

(
±
,

U

)

{\mathbf {a}}\in H^2(\pm , {\mathbb {U}})

gives rise to a double covering of

Q

(

ζ
∞

)

/

Q

{\mathbb {Q}}(\zeta _ \infty )/{\mathbb {Q}}

, by

Q

(

ζ
∞

,

sin
⁡

a

)

/

Q

(

ζ
∞

)

{\mathbb {Q}}(\zeta _ \infty ,\sqrt {\sin {\mathbf {a}}})/{\mathbb {Q}}(\zeta _ \infty )

. When

a

{\mathbf {a}}

lifts a canonical basis element indexed by two odd primes, we show that this double covering can be non-abelian. However, if

a

{\mathbf {a}}

represents any of the canonical basis classes indexed by an odd squarefree positive integer divisible by at least four primes, then the Galois group of

Q

(

ζ
∞

,

sin
⁡

a

)

/

Q

{\mathbb {Q}}(\zeta _ \infty ,\sqrt {\sin {\mathbf {a}}})/{\mathbb {Q}}

is abelian and hence

sin
⁡

a

∈

Q

(

ζ
∞

)

\sqrt {\sin {\mathbf {a}}} \in {\mathbb {Q}}(\zeta _ \infty )

. The

sin
⁡

a

\sqrt {\sin {\mathbf {a}}}

may very well be a new supply of abelian units. The relevance of these units to the unit index formula for cyclotomic fields calls for further investigations.
The Jantzen sum formula for cyclotomic 𝑞–Schur algebras
Authors: James Gordon , Mathas Andrew
Published: July 2002

The cyclotomic

q
q

-Schur algebra was introduced by Dipper, James and Mathas, in order to provide a new tool for studying the Ariki-Koike algebra. We here prove an analogue of Jantzen’s sum formula for the cyclotomic

q
q

-Schur algebra. Among the applications is a criterion for certain Specht modules of the Ariki-Koike algebras to be irreducible.
Infinitely Renormalizable Quadratic Polynomials
Authors: Jiang Yunping
Published: July 2002

We prove that the Julia set of a quadratic polynomial which admits an infinite sequence of unbranched, simple renormalizations with complex bounds is locally connected. The method in this study is three-dimensional puzzles.
Dihedral coverings of algebraic surfaces and their application
Authors: Tokunaga Hiro-o
Published: July 2002

In this article, we study dihedral coverings of algebraic surfaces branched along curves with at most simple singularities. A criterion for a reduced curve to be the branch locus of some dihedral covering is given. As an application we have the following: Let

B
B

be a reduced plane curve of even degree

d
d

having only

a
a

nodes and

b
b

cusps. If

2
a
+
6
b
>
2

d
2

−
6
d
+
6

2a + 6b > 2d^2 - 6d + 6

, then

π
1

(

P

2

∖
B
)

\pi _1(\mathbf {P}^2 \setminus B)

is non-abelian. Note that Nori’s result implies that

π
1

(

P

2

∖
B
)

\pi _1(\mathbf {P}^2 \setminus B)

is abelian, provided that

2
a
+
6
b
>

d
2

2a + 6b > d^2

.
Scattering matrices for the quantum 𝑁 body problem
Authors: Hassell Andrew
Published: July 2002

Let

H
H

be a generalized

N
N

body Schrödinger operator with very short range potentials. Using Melrose’s scattering calculus, it is shown that the free channel ‘geometric’ scattering matrix, defined via asymptotic expansions of generalized eigenfunctions of

H
H

, coincides (up to normalization) with the free channel ‘analytic’ scattering matrix defined via wave operators. Along the way, it is shown that the free channel generalized eigenfunctions of Herbst-Skibsted and Jensen-Kitada coincide with the plane waves constructed by Hassell and Vasy and if the potentials are very short range.
Principal curvatures of isoparametric hypersurfaces in ℂℙⁿ
Authors: Xiao Liang
Published: July 2002

Let

M
M

be an isoparametric hypersurface in

C

P

n

\mathbb {C}P^{n}

, and

M
¯

\overline {M}

the inverse image of

M
M

under the Hopf map. By using the relationship between the eigenvalues of the shape operators of

M
M

and

M
¯

\overline {M}

, we prove that

M
M

is homogeneous if and only if either

g
g

or

l
l

is constant, where

g
g

is the number of distinct principal curvatures of

M
M

and

l
l

is the number of non-horizontal eigenspaces of the shape operator on

M
¯

\overline {M}

.
On the asymptotic geometry of nonpositively curved graphmanifolds
Authors: Buyalo S. , Schroeder V.
Published: July 2002

In this paper we study the Tits geometry of a 3-dimensional graphmanifold of nonpositive curvature. In particular we give an optimal upper bound for the length of nonstandard components of the Tits metric. In the special case of a

π

/

2

\pi /2

-metric we determine the whole length spectrum of the nonstandard components.
Definably simple groups in o-minimal structures
Authors: Peterzil Y. , Pillay A. , Starchenko S.
Published: July 2002

Let

G

=
⟨
G
,
⋅
⟩

\mathbb {G}=\langle G, \cdot \rangle

be a group definable in an o-minimal structure

M

\mathcal {M}

. A subset

H
H

of

G
G

is

G

\mathbb {G}

-definable if

H
H

is definable in the structure

⟨
G
,
⋅
⟩

\langle G,\cdot \rangle

(while definable means definable in the structure

M

\mathcal {M}

). Assume

G

\mathbb {G}

has no

G

\mathbb {G}

-definable proper subgroup of finite index. In this paper we prove that if

G

\mathbb {G}

has no nontrivial abelian normal subgroup, then

G

\mathbb {G}

is the direct product of

G

\mathbb {G}

-definable subgroups

H
1

,
…
,

H
k

H_1,\ldots ,H_k

such that each

H
i

H_i

is definably isomorphic to a semialgebraic linear group over a definable real closed field. As a corollary we obtain an o-minimal analogue of Cherlin’s conjecture.
Strongly almost disjoint sets and weakly uniform bases
Authors: Balogh Z. , Davis S. , Just W. , Shelah S. , Szeptycki P.
Published: July 2002

A combinatorial principle CECA is formulated and its equivalence with GCH + certain weakenings of

◻

λ

\Box _\lambda

for singular

λ
\lambda

is proved. CECA is used to show that certain “almost point-

>
τ

>\tau

” families can be refined to point-

>
τ

> \tau

families by removing a small set from each member of the family. This theorem in turn is used to show the consistency of “every first countable

T
1

T_1

-space with a weakly uniform base has a point-countable base.”
A classification of one dimensional almost periodic tilings arising from the projection method
Authors: Mingo James
Published: July 2002

For each irrational number

α
\alpha

, with continued fraction expansion

[
0
;

a
1

,

a
2

,

a
3

,
…
]

[0; a_1, a_2,a_3, \dots ]

, we classify, up to translation, the one dimensional almost periodic tilings which can be constructed by the projection method starting with a line of slope

α
\alpha

. The invariant is a sequence of integers in the space
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper X Subscript alpha Baseline equals left-brace left-parenthesis x Subscript i Baseline right-parenthesis Subscript i equals 1 Superscript normal infinity Baseline bar x Subscript i Baseline element-of StartSet 0 comma 1 comma 2 comma ellipsis comma a Subscript i Baseline EndSet">

X
α

=
{
(

x
i

)

i
=
1

∞

∣

x
i

∈
{
0
,
1
,
2
,
…
,

a
i

}

X_\alpha = \{(x_i)_{i=1}^\infty \mid x_i \in \{0,1,2, \dots ,a_i\}

and

x

i
+
1

=
0

x_{i+1} = 0

whenever

x
i

=

a
i

}

x_i = a_i\}

modulo the equivalence relation generated by tail equivalence and
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis a 1 comma 0 comma a 3 comma 0 comma ellipsis right-parenthesis tilde left-parenthesis 0 comma a 2 comma 0 comma a 4 comma ellipsis right-parenthesis tilde left-parenthesis a 1 minus 1 comma a 2 minus 1 comma a 3 minus 1 comma ellipsis right-parenthesis">

(

a
1

,
0
,

a
3

,
0
,
…
)
∼
(
0
,

a
2

,
0
,

a
4

,
…
)
∼
(

a
1

−
1
,

a
2

−
1
,

a
3

−
1
,
…
)

(a_1, 0, a_3, 0, \dots ) \sim (0, a_2, 0, a_4, \dots ) \sim (a_1 -1, a_2 - 1, a_3 - 1, \dots )

. Each tile in a tiling

T

\textsf {T}

, of slope

α
\alpha

, is coded by an integer

0
≤
x
≤
[
α
]

0 \leq x \leq [\alpha ]

. Using a composition operation, we produce a sequence of tilings

T

1

=

T

,

T

2

,

T

3

,
…

\textsf {T}_1 = \textsf {T}{}, \textsf {T}_2, \textsf {T}_3, \dots

. Each tile in

T

i

\textsf {T}_i

gets absorbed into a tile in

T

i
+
1

\textsf {T}_{i+1}

. A choice of a starting tile in

T

1

\textsf {T}_1

will thus produce a sequence in

X
α

X_\alpha

. This is the invariant.
Relative Embedding Problems
Authors: Black Elena , Swallow John
Published: July 2002

We consider Galois embedding problems

G
↠
H
≅
Gal
⁡
(
X

/

Z
)

G\twoheadrightarrow H\cong \operatorname {Gal}(X/Z)

such that a Galois embedding problem

G
↠
Gal
⁡
(
Y

/

Z
)

G\twoheadrightarrow \operatorname {Gal}(Y/Z)

is solvable, where

Y

/

Z

Y/Z

is a Galois subextension of

X

/

Z

X/Z

. For such embedding problems with abelian kernel, we prove a reduction theorem, first in the general case of commutative

k
k

-algebras, then in the more specialized field case. We demonstrate with examples of dihedral embedding problems that the reduced embedding problem is frequently of smaller order. We then apply these results to the theory of obstructions to central embedding problems, considering a notion of quotients of central embedding problems, and classify the infinite towers of metacyclic

p
p

-groups to which the reduction theorem applies.
A model for the homotopy theory of homotopy theory
Authors: Rezk Charles
Published: July 2002

We describe a category, the objects of which may be viewed as models for homotopy theories. We show that for such models, “functors between two homotopy theories form a homotopy theory”, or more precisely that the category of such models has a well-behaved internal hom-object.
Multiplier ideals of monomial ideals
Authors: Howald J.
Published: July 2002

In this note we discuss a simple algebraic calculation of the multiplier ideal associated to a monomial ideal in affine

n
n

-space. We indicate how this result allows one to compute not only the multiplier ideal but also the log canonical threshold of an ideal in terms of its Newton polygon.
A model structure on the category of pro-simplicial sets
Authors: Isaksen Daniel
Published: July 2002

We study the category pro-

S
S

\mathcal {SS}

of pro-simplicial sets, which arises in étale homotopy theory, shape theory, and pro-finite completion. We establish a model structure on pro-

S
S

\mathcal {SS}

so that it is possible to do homotopy theory in this category. This model structure is closely related to the strict structure of Edwards and Hastings. In order to understand the notion of homotopy groups for pro-spaces we use local systems on pro-spaces. We also give several alternative descriptions of weak equivalences, including a cohomological characterization. We outline dual constructions for ind-spaces.
On supports and associated primes of modules over the enveloping algebras of nilpotent Lie algebras
Authors: Širola Boris
Published: July 2002

Let

n

\mathfrak n

be a nilpotent Lie algebra, over a field of characteristic zero, and

U

\mathcal U

its universal enveloping algebra. In this paper we study: (1) the prime ideal structure of

U

\mathcal U

related to finitely generated

U

\mathcal U

-modules

V
V

, and in particular the set

Ass
⁡
V

\operatorname {Ass}V

of associated primes for such

V
V

(note that now

Ass
⁡
V

\operatorname {Ass}V

is equal to the set

Annspec
⁡
V

\operatorname {Annspec}V

of annihilator primes for

V
V

); (2) the problem of nontriviality for the modules

V

/

P

V

V/\mathcal PV

when

P

\mathcal P

is a (maximal) prime of

U

\mathcal U

, and in particular when

P

\mathcal P

is the augmentation ideal

U

n

\mathcal U\mathfrak n

of

U

\mathcal U

. We define the support of

V
V

, as a natural generalization of the same notion from commutative theory, and show that it is the object of primary interest when dealing with (2). We also introduce and study the reduced localization and the reduced support, which enables to better understand the set

Ass
⁡
V

\operatorname {Ass}V

. We prove the following generalization of a stability result given by W. Casselman and M. S. Osborne in the case when

N

\mathfrak N

,

N

\mathfrak N

as in the theorem, are abelian. We also present some of its interesting consequences.

Theorem. Let

Q

\mathfrak Q

be a finite-dimensional Lie algebra over a field of characteristic zero, and

N

\mathfrak N

an ideal of

Q

\mathfrak Q

; denote by

U
(

N

)

U(\mathfrak N)

the universal enveloping algebra of

N

\mathfrak N

. Let

V
V

be a

Q

\mathfrak Q

-module which is finitely generated as an

N

\mathfrak N

-module. Then every annihilator prime of

V
V

, when

V
V

is regarded as a

U
(

N

)

U(\mathfrak N)

-module, is

Q

\mathfrak Q

-stable for the adjoint action of

Q

\mathfrak Q

on

U
(

N

)

U(\mathfrak N)

.
Block representation type of reduced enveloping algebras
Authors: Gordon Iain , Premet Alexander
Published: July 2002

Let

K
K

be an algebraically closed field of characteristic

p
p

,

G
G

a connected, reductive

K
K

-group,

g

=
Lie
(
G
)

\mathfrak {g}=\text {Lie}(G)

,

χ
∈

g

∗

\chi \in \mathfrak {g}^*

and

U
χ

(

g

)

U_\chi (\mathfrak {g})

the reduced enveloping algebra of

g

\mathfrak {g}

associated with

χ
\chi

. Assume that

G

(
1
)

G^{(1)}

is simply-connected,

p
p

is good for

G
G

and

g

\mathfrak {g}

has a non-degenerate

G
G

-invariant bilinear form. All blocks of

U
χ

(

g

)

U_\chi (\mathfrak {g})

having finite and tame representation type are determined.
Dynamics of implicit operations and tameness of pseudovarieties of groups
Authors: Almeida Jorge
Published: July 2002

This work gives a new approach to the construction of implicit operations. By considering “higher-dimensional” spaces of implicit operations and implicit operators between them, the projection of idempotents back to one-dimensional spaces produces implicit operations with interesting properties. Besides providing a wealth of examples of implicit operations which can be obtained by these means, it is shown how they can be used to deduce from results of Ribes and Zalesskiĭ, Margolis, Sapir and Weil, and Steinberg that the pseudovariety of

p
p

-groups is tame. More generally, for a recursively enumerable extension closed pseudovariety of groups

V

\mathbf {V}

, if it can be decided whether a finitely generated subgroup of the free group with the pro-

V

\mathbf {V}

topology is dense, then

V

\mathbf {V}

is tame.
Verlinde bundles and generalized theta linear series
Authors: Popa Mihnea
Published: July 2002

In this paper we approach the study of generalized theta linear series on moduli of vector bundles on curves via vector bundle techniques on abelian varieties.

We study a naturally defined class of vector bundles on a Jacobian, called Verlinde bundles, in order to obtain information about duality between theta functions and effective global and normal generation on these moduli spaces.
Principal bundles over a projective scheme
Authors: Hyeon Donghoon
Published: July 2002

We prove the existence of a quasi-projective moduli scheme for principal bundles over an arbitrary projective scheme.
Convergence of two-dimensional weighted integrals
Authors: Pramanik Malabika
Published: July 2002

A two-dimensional weighted integral in

R

2

\mathbb R^{2}

is proposed as a tool for analyzing higher-dimensional unweighted integrals, and a necessary and sufficient condition for the finiteness of the weighted integral is obtained.