bluuebunny/crossref_metadata_2025 huggingface dataset:
Centralizers of Iwahori-Hecke algebras
Authors: Francis Andrew
Published: July 2002

To date, integral bases for the centre of the Iwahori-Hecke algebra of a finite Coxeter group have relied on character theoretical results and the isomorphism between the Iwahori-Hecke algebra when semisimple and the group algebra of the finite Coxeter group. In this paper, we generalize the minimal basis approach of an earlier paper, to provide a way of describing and calculating elements of the minimal basis for the centre of an Iwahori-Hecke algebra which is entirely combinatorial in nature, and independent of both the above mentioned theories. This opens the door to further generalization of the minimal basis approach to other cases. In particular, we show that generalizing it to centralizers of parabolic subalgebras requires only certain properties in the Coxeter group. We show here that these properties hold for groups of type

A
A

and

B
B

, giving us the minimal basis theory for centralizers of any parabolic subalgebra in these types of Iwahori-Hecke algebra.
Complexifications of symmetric spaces and Jordan theory
Authors: Bertram Wolfgang
Published: July 2002

Generalizing Hermitian and pseudo-Hermitian spaces, we define twisted complex symmetric spaces, and we show that they correspond to an algebraic object called Hermitian Jordan triple products. The main topic of this work is to investigate the class of real forms of twisted complex symmetric spaces, called the category of symmetric spaces with twist. We show that this category is equivalent to the category of all real Jordan triple systems, and we can use a work of B.O. Makarevič in order to classify the irreducible spaces. The classification shows that most irreducible symmetric spaces have exactly one twisted complexification. This leads to open problems concerning the relation of Jordan and Lie triple systems.
Nonradial Hörmander algebras of several variables and convolution operators
Authors: Bonet José , Galbis Antonio , Momm Siegfried
Published: July 2002

A characterization of the closed principal ideals in nonradial Hörmander algebras of holomorphic functions of several variables in terms of the behaviour of the generator is obtained. This result is applied to study the range of convolution operators and ultradifferential operators on spaces of quasianalytic functions of Beurling type. Contrary to what is known to happen in the case of non-quasianalytic functions, an ultradistribution on a space of quasianalytic functions is constructed such that the range of the operator does not contain the real analytic functions.
Invariant ideals of abelian group algebras and representations of groups of Lie type
Authors: Passman D. , Zalesskiĭ A.
Published: July 2002

This paper contributes to the general study of ideal lattices in group algebras of infinite groups. In recent years, the second author has extensively studied this problem for

G
G

an infinite locally finite simple group. It now appears that the next stage in the general problem is the case of abelian-by-simple groups. Some basic results reduce this problem to that of characterizing the ideals of abelian group algebras stable under certain (simple) automorphism groups. Here we begin the analysis in the case where the abelian group

A
A

is the additive group of a finite-dimensional vector space

V
V

over a locally finite field

F
F

of prime characteristic

p
p

, and the automorphism group

G
G

is a simple infinite absolutely irreducible subgroup of

G
L
(
V
)

GL(V)

. Thus

G
G

is isomorphic to an infinite simple periodic group of Lie type, and

G
G

is realized in

G
L
(
V
)

GL(V)

via a twisted tensor product

ϕ
\phi

of infinitesimally irreducible representations. If

S
S

is a Sylow

p
p

-subgroup of

G
G

and if

⟨
v
⟩

\langle v\rangle

is the unique line in

V
V

stabilized by

S
S

, then the approach here requires a precise understanding of the linear character associated with the action of a maximal torus

T
G

T_G

on

⟨
v
⟩

\langle v\rangle

. At present, we are able to handle the case where

ϕ
\phi

is a rational representation with character field equal to

F
F

.
Construction de certaines opérades et bigèbres associées aux polytopes de Stasheff et hypercubes
Authors: Chapoton Frédéric
Published: July 2002

Stasheff polytopes, introduced by Stasheff in his study of

H
H

-spaces, are linked to associativity. The direct sum of their cellular complexes is the underlying complex of the

A

∞

A_{\infty }

operad which describes homotopy associative algebras. In particular, there exists a quasi-isomorphism

A

∞

→
As

A_{\infty }\rightarrow \operatorname {As}

.

Here, we define on the direct sum of their dual cellular complexes the structure of a differential graded operad. This construction extends the dendriform operad of Loday, which corresponds to the vertices of the polytopes. We also define the structure of a differential graded operad on the direct sum of the dual cellular complexes of the hypercubes. We define a quasi-isomorphism from

As
\operatorname {As}

to each of these operads.

We also define non-differential variants of the two preceding operads and a morphism from

As
\operatorname {As}

to each of these operads. We show that the free algebras have a coproduct which turns them into bialgebras.

Résumé. Les polytopes de Stasheff, introduits pour l’étude des

H
H

-espaces, sont liés à l’associativité. La somme directe de leurs complexes cellulaires forme le complexe sous-jacent à l’opérade

A
∞

A_\infty

qui décrit les algèbres associatives à homotopie près. En particulier, il existe un quasi-isomorphisme

A
∞

→
As

A_\infty \to \operatorname {As}

.

Ici, on munit la somme directe des duaux de leurs complexes cellulaires d’une structure d’opérade différentielle graduée. Cette construction généralise l’opérade des algèbres dendriformes de Loday, qui correspond aux sommets des polytopes. On munit aussi la somme directe des duaux des complexes cellulaires des hypercubes d’une structure d’opérade différentielle graduée. On définit un quasi-isomorphisme de

As
\operatorname {As}

dans chacune de ces deux opérades.

On construit également des variantes non différentielles des deux opérades précédentes. On définit un morphisme de

As
\operatorname {As}

dans chacune de ces opérades et on montre que les algèbres libres sont munies d’un coproduit coassociatif qui en fait des bigèbres.
The extraspecial case of the 𝑘(𝐺𝑉) problem
Authors: Gluck David , Magaard Kay
Published: July 2002

Let

E
E

be an extraspecial-type group and

V
V

a faithful, absolutely irreducible

k
[
E
]

k[E]

-module, where

k
k

is a finite field. Let

G
G

be the normalizer in

G
L
(
V
)

GL(V)

of

E
E

. We show that, with few exceptions, there exists a

v
∈
V

v\in V

such that the restriction of

V
V

to

C
H

(
v
)

C_H(v)

is self-dual whenever

H
≤
G

H\le G

and

(
|
H
|
,
|
V
|
)
=
1

(\vert H\vert , \vert V\vert )=1

.
Subgroup properties of fully residually free groups
Authors: Kapovich Ilya
Published: July 2002

We prove that fully residually free groups have the Howson property, that is the intersection of any two finitely generated subgroups in such a group is again finitely generated. We also establish some commensurability properties for finitely generated fully residually free groups which are similar to those of free groups. Finally we prove that for a finitely generated fully residually free group the membership problem is solvable with respect to any finitely generated subgroup.
Localisation homotopique et tour de Taylor pour une catégorie abélienne
Authors: Renaudin Olivier
Published: July 2002

On indique comment une sous-catégorie colocalisante d’une catégorie abélienne induit une localisation dans la catégorie dérivé. Ceci permet une nouvelle construction de la tour de Taylor d’un foncteur à valeur dans une catégorie de module.
Intertwining operator superalgebras and vertex tensor categories for superconformal algebras, II
Authors: Huang Yi-Zhi , Milas Antun
Published: July 2002

We construct the intertwining operator superalgebras and vertex tensor categories for the

N
=
2

N=2

superconformal unitary minimal models and other related models.
Nonradial solvability structure of super-diffusive nonlinear parabolic equations
Authors: Daskalopoulos Panagiota , del Pino Manuel
Published: July 2002

We study the solvability of the Cauchy problem for the nonlinear parabolic equation
\[

∂
u

∂
t

=

div

(

u

m
−
1

∇
u
)

\frac {\partial u}{\partial t} = \mbox {div}\, (u^{m-1}\nabla u)

\]
when

m
>
0

m > 0

in

R

2

\textbf {R}^2

, with

u
(
x
,
0
)
=
f
(
x
)

u(x,0)= f(x)

a given nonnegative function. It is known from earlier works of the authors that the asymptotic radial growth

r

−
2

/

1
−
m

r^{-2/1-m}

,

r
=

|

x

|

r=|x|

for the spherical averages of

f
(
x
)

f(x)

is critical for local solvability, in particular ensuring it if

f
f

is radially symmetric. We show that if the initial data

f
(
x
)

f(x)

behaves in polar coordinates like

r

−
2

/

1
−
m

g
(
θ
)

r^{-2/1-m} g(\theta )

, for large

r
=

|

x

|

r= |x|

with

g
g

nonnegative and

2
π

2\pi

-periodic, then the following holds: If

g
g

vanishes on some interval of length

l
∗

=

(
m
−
1
)
π

2
m

>
0

l^* = \frac {(m-1)\pi }{2m} >0

, then there is no local solution of the initial value problem. On the other hand, if such an interval does not exist, then the initial value problem is locally solvable and the time of existence can be estimated explicitly.
Wandering orbit portraits
Authors: Kiwi Jan
Published: July 2002

We study a counting problem in holomorphic dynamics related to external rays of complex polynomials. We give upper bounds on the number of external rays that land at a point

z
z

in the Julia set of a polynomial, provided that

z
z

has an infinite forward orbit.
The super order dual of an ordered vector space and the Riesz–Kantorovich formula
Authors: Aliprantis Charalambos , Tourky Rabee
Published: July 2002

A classical theorem of F. Riesz and L. V. Kantorovich asserts that if

L
L

is a vector lattice and

f
f

and

g
g

are order bounded linear functionals on

L
L

, then their supremum (least upper bound)

f
∨
g

f\lor g

exists in

L
∼

L^\sim

and for each

x
∈

L
+

x\in L_+

it satisfies the so-called Riesz–Kantorovich formula:
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-bracket f logical-or g right-bracket left-parenthesis x right-parenthesis equals sup left-brace f left-parenthesis y right-parenthesis plus g left-parenthesis z right-parenthesis colon y comma z element-of upper L Subscript plus Baseline normal a normal n normal d y plus z equals x right-brace period">

[

f
∨
g

]

(
x
)
=
sup

{

f
(
y
)
+
g
(
z
)
:
 
y
,
z
∈

L
+

 

a
n
d

 

y
+
z
=
x

}

.

\bigl [f\lor g\bigr ](x)=\sup \bigl \{f(y)+g(z)\colon \ y,z\in L_+\ \,\mathrm {and}\ \, y+z=x\bigr \}\,.

\]
Related to the Riesz–Kantorovich formula is the following long-standing problem: If the supremum of two order bounded linear functionals

f
f

and

g
g

on an ordered vector space exists, does it then satisfy the Riesz–Kantorovich formula?

In this paper, we introduce an extension of the order dual of an ordered vector space and provide some answers to this long-standing problem. The ideas regarding the Riesz–Kantorovich formula owe their origins to the study of the fundamental theorems of welfare economics and the existence of competitive equilibrium. The techniques introduced here show that the existence of decentralizing prices for efficient allocations is closely related to the above-mentioned problem and to the properties of the Riesz–Kantorovich formula.
Gaussian bounds for derivatives of central Gaussian semigroups on compact groups
Authors: Bendikov A. , Saloff-Coste L.
Published: July 2002

For symmetric central Gaussian semigroups on compact connected groups, assuming the existence of a continuous density, we show that this density admits space derivatives of all orders in certain directions. Under some additional assumptions, we prove that these derivatives satisfy certain Gaussian bounds.
A semigroup of operators in convexity theory
Authors: Kiselman Christer
Published: July 2002

We consider three operators which appear naturally in convexity theory and determine completely the structure of the semigroup generated by them.

Resumo. Duongrupo de operatoroj en la teorio pri konvekseco. Ni konsideras tri operatorojn kiuj aperas nature en la teorio pri konvekseco kaj plene determinas la strukturon de la duongrupo generita de ili.
Certain imprimitive reflection groups and their generic versions
Authors: Shi Jian-yi
Published: July 2002

The present paper is concerned with the connection between the imprimitive reflection groups

G
(
m
,
m
,
n
)

G(m,m,n)

,

m
∈

N

m\in \mathbb {N}

, and the affine Weyl group

A
~

n
−
1

\widetilde {A}_{n-1}

. We show that

A
~

n
−
1

\widetilde {A}_{n-1}

is a generic version of the groups

G
(
m
,
m
,
n
)

G(m,m,n)

,

m
∈

N

m\in \mathbb {N}

. We introduce some new presentations of these groups which are shown to have some group-theoretic advantages. Then we define the Hecke algebras of these groups and of their braid versions, each in two ways according to two presentations. Finally we give a new description for the affine root system

Φ
¯

\overline {\Phi }

of

A
~

n
−
1

\widetilde {A}_{n-1}

such that the action of

A
~

n
−
1

\widetilde {A}_{n-1}

on

Φ
¯

\overline {\Phi }

is compatible with that of

G
(
m
,
m
,
n
)

G(m,m,n)

on its root system in some sense.
On loop spaces of configuration spaces
Authors: Cohen F. , Gitler S.
Published: July 2002

This article gives an analysis of topological and homological properties for loop spaces of configuration spaces. The main topological results are given by certain choices of product decompositions of these spaces, as well as “twistings" between the factors. The main homological results are given in terms of extensions of the “infinitesimal braid relations" or “universal Yang-Baxter Lie relations".
A Concordance Extension Theorem
Authors: Jones Joel
Published: July 2002

Let

p

E
→
B

p\:E\to B

be a manifold approximate fibration between closed manifolds, where

dim
⁡
(
E
)
≥
4

\dim (E)\ge 4

, and let

M
(
p
)

M(p)

be the mapping cylinder of

p
p

. In this paper it is shown that if

g

B
×
I
→
B
×
I

g\: B\times I\to B\times I

is any concordance on

B
B

, then there exists a concordance

G

M
(
p
)
×
I
→
M
(
p
)
×
I

G\:M(p)\times I \to M(p)\times I

such that

G

|

B
×
I
=
g

G|B\times I=g

and

G

|

E
×
{
0
}
×
I
=
i

d

E
×
I

G|E\times \{0\}\times I= id_{E\times I}

. As an application, if

N
n

N^n

and

M

n
+
j

M^{n+j}

are closed manifolds where

N
N

is a locally flat submanifold of

M
M

and

n
≥
5

n\ge 5

and

j
≥
1

j\ge 1

, then a concordance

g

N
×
I
→
N
×
I

g\: N\times I\to N\times I

extends to a concordance

G

M
×
I
→
M
×
I

G\:M\times I\to M\times I

on

M
M

such that

G

|

N
×
I
=
g

G|N\times I=g

. This uses the fact that under these hypotheses there exists a manifold approximate fibration

p

E
→
N

p\: E\to N

, where

E
E

is a closed

(
n
+
j
−
1
)

(n+j-1)

-manifold, such that the mapping cylinder

M
(
p
)

M(p)

is homeomorphic to a closed neighborhood of

N
N

in

M
M

by a homeomorphism which is the identity on

N
N

.
Factorizations of simple algebraic groups
Authors: Liebeck Martin , Saxl Jan , Seitz Gary
Published: July 2002

We determine all factorizations of simple algebraic groups as the product of two maximal closed connected subgroups. Additional results are established which drop the maximality assumption, and applications are given to the study of subgroups of classical groups transitive on subspaces of a given dimension.
Affine Dupin Surfaces
Authors: Niebergall Ross , Ryan Patrick
Published: July 2002

In this paper we study nondegenerate affine surfaces in

R

3

\mathbb {R} ^{3}

whose affine principal curvatures are constant along their lines of curvature. We give a complete local classification of these surfaces assuming that the lines of curvature are planar, and there are no umbilics.
Second Root Vectors for Multiparameter Eigenvalue Problems of Fredholm Type
Authors: Binding Paul , Kosir Tomaz
Published: July 2002

A class of multiparameter eigenvalue problems involving (generally) non self-adjoint and unbounded operators is studied. A basis for the second root subspace, at eigenvalues of Fredholm type, is computed in terms of the underlying multiparameter system. A self-adjoint version of this result is given under a weak definiteness condition, and Sturm-Liouville and finite-dimensional examples are considered.
Real analysis related to the Monge-Ampère equation
Authors: Caffarelli Luis , Gutiérrez Cristian
Published: July 2002

In this paper we consider a family of convex sets in

R

n

\mathbf {R}^{n}

,

F

=
{
S
(
x
,
t
)
}

\mathcal {F}= \{S(x,t)\}

,

x
∈

R

n

x\in \mathbf {R}^{n}

,

t
>
0

t>0

, satisfying certain axioms of affine invariance, and a Borel measure

μ
\mu

satisfying a doubling condition with respect to the family

F

.

\mathcal {F}.

The axioms are modelled on the properties of the solutions of the real Monge-Ampère equation. The purpose of the paper is to show a variant of the Calderón-Zygmund decomposition in terms of the members of

F

.

\mathcal {F}.

This is achieved by showing first a Besicovitch-type covering lemma for the family

F

\mathcal {F}

and then using the doubling property of the measure

μ
.

\mu .

The decomposition is motivated by the study of the properties of the linearized Monge-Ampère equation. We show certain applications to maximal functions, and we prove a John and Nirenberg-type inequality for functions with bounded mean oscillation with respect to

F

.

\mathcal {F}.
Rotation Vectors and Fixed Points of Area Preserving Surface Diffeomorphisms
Authors: Franks John
Published: July 2002

We consider the (homological) rotation vectors for area preserving diffeomorphisms of compact surfaces which are homotopic to the identity. There are two main results. The first is that if

0
0

is in the interior of the convex hull of the rotation vectors for such a diffeomorphism then

f
f

has a fixed point of positive index. The second result asserts that if

f
f

has a vanishing mean rotation vector then

f
f

has a fixed point of positive index. There are several applications including a new proof of the Arnold conjecture for area preserving diffeomorphisms of compact surfaces.
On 𝐶𝑅-mappings between algebraic Cauchy-Riemann manifolds and separate algebraicity for holomorphic functions
Authors: Sharipov Ruslan , Sukhov Alexander
Published: July 2002

We prove the algebraicity of smooth

C
R

CR

-mappings between algebraic Cauchy-Riemann manifolds. A generalization of separate algebraicity principle is established.
The Morse spectrum of linear flows on vector bundles
Authors: Colonius Fritz , Kliemann Wolfgang
Published: July 2002

For a linear flow

Φ
\Phi

on a vector bundle

π
:
E
→
S

\pi : E \rightarrow S

a spectrum can be defined in the following way: For a chain recurrent component

M

\mathcal {M}

on the projective bundle

P

E

\mathbb {P} E

consider the exponential growth rates associated with (finite time)

(
ε
,
T
)

(\varepsilon ,T)

-chains in

M

\mathcal {M}

, and define the Morse spectrum

Σ

M
o

(

M

,
Φ
)

\Sigma _{Mo}(\mathcal {M},\Phi )

over

M

\mathcal {M}

as the limits of these growth rates as

ε
→
0

\varepsilon \rightarrow 0

and

T
→
∞

T \rightarrow \infty

. The Morse spectrum

Σ

M
o

(
Φ
)

\Sigma _{Mo}(\Phi )

of

Φ
\Phi

is then the union over all components

M

⊂

P

E

\mathcal {M}\subset \mathbb {P}E

. This spectrum is a synthesis of the topological approach of Selgrade and Salamon/Zehnder with the spectral concepts based on exponential growth rates, such as the Oseledec̆ spectrum or the dichotomy spectrum of Sacker/Sell. It turns out that

Σ

M
o

(
Φ
)

\Sigma _{Mo}(\Phi )

contains all Lyapunov exponents of

Φ
\Phi

for arbitrary initial values, and the

Σ

M
o

(

M

,
Φ
)

\Sigma _{Mo}(\mathcal {M},\Phi )

are closed intervals, whose boundary points are actually Lyapunov exponents. Using the fact that

Φ
\Phi

is cohomologous to a subflow of a smooth linear flow on a trivial bundle, one can prove integral representations of all Morse and all Lyapunov exponents via smooth ergodic theory. A comparison with other spectral concepts shows that, in general, the Morse spectrum is contained in the topological spectrum and the dichotomy spectrum, but the spectral sets agree if the induced flow on the base space is chain recurrent. However, even in this case, the associated subbundle decompositions of

E
E

may be finer for the Morse spectrum than for the dynamical spectrum. If one can show that the (closure of the) Floquet spectrum (i.e. the Lyapunov spectrum based on periodic trajectories in

P

E

\mathbb {P} E

) agrees with the Morse spectrum, then one obtains equality for the Floquet, the entire Oseledeč, the Lyapunov, and the Morse spectrum. We present an example (flows induced by

C

∞

C^{\infty }

vector fields with hyperbolic chain recurrent components on the projective bundle) where this fact can be shown using a version of Bowen’s Shadowing Lemma.
Hardy spaces and twisted sectors for geometric models
Authors: Poggi-Corradini Pietro
Published: July 2002

We study the one-to-one analytic maps

σ
\sigma

that send the unit disc into a region

G
G

with the property that

λ
G
⊂
G

\lambda G\subset G

for some complex number

λ
\lambda

,

0
>

|

λ

|

>
1

0>|\lambda |>1

. These functions arise in iteration theory, giving a model for the self-maps of the unit disk into itself, and in the study of composition operators as their eigenfunctions. We show that for such functions there are geometrical conditions on the image region

G
G

that characterize their rate of growth, i.e. we prove that

σ
∈

⋂

p
>
∞

H
p

\sigma \in \bigcap _{p>\infty }H^p

if and only if

G
G

does not contain a twisted sector. Then, we examine the connection with composition operators, and further investigate the no twisted sector condition. Finally, in the Appendix, we give a different proof of a result of J. Shapiro about the essential norm of a composition operator.
The behavior of Fourier transforms for nilpotent Lie groups
Authors: Lipsman Ronald , Rosenberg Jonathan
Published: July 2002

We study weak analogues of the Paley-Wiener Theorem for both the scalar-valued and the operator-valued Fourier transforms on a nilpotent Lie group

G
G

. Such theorems should assert that the appropriate Fourier transform of a function or distribution of compact support on

G
G

extends to be “holomorphic” on an appropriate complexification of (a part of)

G
^

\hat G

. We prove the weak scalar-valued Paley-Wiener Theorem for some nilpotent Lie groups but show that it is false in general. We also prove a weak operator-valued Paley-Wiener Theorem for arbitrary nilpotent Lie groups, which in turn establishes the truth of a conjecture of Moss. Finally, we prove a conjecture about Dixmier-Douady invariants of continuous-trace subquotients of

C

∗

(
G
)

C^{*}(G)

when

G
G

is two-step nilpotent.
Operator Semigroup Compactifications
Authors: Junghenn H.
Published: July 2002

A weakly continuous, equicontinuous representation of a semitopological semigroup

S
S

on a locally convex topological vector space

X
X

gives rise to a family of operator semigroup compactifications of

S
S

, one for each invariant subspace of

X
X

. We consider those invariant subspaces which are maximal with respect to the associated compactification possessing a given property of semigroup compactifications and show that under suitable hypotheses this maximality is preserved under the formation of projective limits, strict inductive limits and tensor products.
R-torsion and zeta functions for analytic Anosov flows on 3-manifolds
Authors: Sánchez-Morgado Héctor
Published: July 2002

We improve previous results relating R-torsion, for an acyclic representation of the fundamental group, with a special value of the torsion zeta function of an analytic Anosov flow on a 3-manifold. By using the new techniques of Rugh and Fried we get rid of the unpleasent assumptions about the regularity of the invariant foliations.
Transfinite multifractal dimension spectrums
Authors: Williams Stanley
Published: July 2002

The first order theory of the decomposition of measures with respect to dimension which has been developed by Kahane, Katznelson, Cutler, and others is extended through transfinite recursion to a

ω
1

\omega _1

-order theory. Necessary and sufficient conditions for a finite regular Borel measure on

[
0
,
d

]

ω
1

[0,d]^{\omega _1}

to be a

ω
1

\omega _1

-order multispectrum for a finite Borel measure on

R

d

\mathbb {R}^d

is given.
Which families of 𝑙-modal maps are full?
Authors: Galeeva R. , van Strien S.
Published: July 2002

In this paper we shall show that certain conditions which are sufficient for a family of one-dimensional maps to be full cannot be dispensed with.
Composition operators between Bergman and Hardy spaces
Authors: Smith Wayne
Published: July 2002

We study composition operators between weighted Bergman spaces. Certain growth conditions for generalized Nevanlinna counting functions of the inducing map are shown to be necessary and sufficient for such operators to be bounded or compact. Particular choices for the weights yield results on composition operators between the classical unweighted Bergman and Hardy spaces.
Rook theory, compositions, and zeta functions
Authors: Haglund James
Published: July 2002

A new family of Dirichlet series having interesting combinatorial properties is introduced. Although they have no functional equation or Euler product, under the Riemann Hypothesis it is shown that these functions have no zeros in

R
e

(
s
)
>
1

/

2

\mathrm {Re}(s)>1/2

. Some identities in the ring of formal power series involving rook theory and continued fractions are developed.
Minimal isometric immersions of inhomogeneous spherical space forms into spheres— a necessary condition for existence
Authors: Escher Christine
Published: July 2002

Although much is known about minimal isometric immersions into spheres of homogeneous spherical space forms, there are no results in the literature about such immersions in the dominant case of inhomogeneous space forms. For a large class of these, we give a necessary condition for the existence of such an immersion of a given degree. This condition depends only upon the degree and the fundamental group of the space form and is given in terms of an explicitly computable function. Evaluating this function shows that neither

L
(
5
,
2
)

L(5,2)

nor

L
(
8
,
3
)

L(8,3)

admit a minimal isometric immersion into any sphere if the degree of the immersion is less than

28
28

, or less than

20
20

, respectively.
On Gelfand-Kirillov Transcendence Degree
Authors: Zhang James
Published: July 2002

We study some basic properties of the Gelfand-Kirillov transcendence degree and compute the transcendence degree of various infinite-dimensional division algebras including quotient division algebras of quantized algebras related to quantum groups, 3-dimensional Artin-Schelter regular algebras and the 4-dimensional Sklyanin algebra.
Packing dimension and Cartesian products
Authors: Bishop Christopher , Peres Yuval
Published: July 2002

We show that for any analytic set

A
A

in

R

d

\mathbf {R}^d

, its packing dimension

dim

P

⁡
(
A
)

\dim _{\mathrm {P}}(A)

can be represented as
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="sup Underscript upper B Endscripts left-brace dimension Subscript normal upper H Baseline left-parenthesis upper A times upper B right-parenthesis minus dimension Subscript normal upper H Baseline left-parenthesis upper B right-parenthesis right-brace comma">

sup
B

{

dim

H

⁡
(
A
×
B
)
−

dim

H

⁡
(
B
)
}

,

\; \sup _B \{ \dim _{\mathrm {H}} (A \times B) -\dim _{\mathrm {H}}(B) \} \, , \,

where the supremum is over all compact sets

B
B

in

R

d

\mathbf {R}^d

, and

dim

H

\dim _{\mathrm {H}}

denotes Hausdorff dimension. (The lower bound on packing dimension was proved by Tricot in 1982.) Moreover, the supremum above is attained, at least if

dim

P

⁡
(
A
)
>
d

\dim _{\mathrm {P}} (A) > d

. In contrast, we show that the dual quantity
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="inf Underscript upper B Endscripts left-brace dimension Subscript normal upper P Baseline left-parenthesis upper A times upper B right-parenthesis minus dimension Subscript normal upper P Baseline left-parenthesis upper B right-parenthesis right-brace comma">

inf
B

{

dim

P

⁡
(
A
×
B
)
−

dim

P

⁡
(
B
)
}

,

\; \inf _B \{ \dim _{\mathrm {P}}(A \times B) -\dim _{\mathrm {P}}(B) \} \, , \,

is at least the “lower packing dimension” of

A
A

, but can be strictly greater. (The lower packing dimension is greater than or equal to the Hausdorff dimension.)
Congruences, Trees, and 𝑝-adic Integers
Authors: Schmidt Wolfgang , Stewart C.
Published: July 2002

Let

f
f

be a polynomial in one variable with integer coefficients, and

p
p

a prime. A solution of the congruence

f
(
x
)
≡
0
(
mod

p
)

f(x) \equiv 0 (\text {mod} \,p)

may branch out into several solutions modulo

p

2

p^{2}

, or it may be extended to just one solution, or it may not extend to any solution. Again, a solution modulo

p

2

p^{2}

may or may not be extendable to solutions modulo

p

3

p^{3}

, etc. In this way one obtains the “solution tree”

T
=
T
(
f
)

T = T(f)

of congruences modulo

p

λ

p^{\lambda }

for

λ
=
1
,
2
,
…

\lambda = 1,2,\ldots

. We will deal with the following questions: What is the structure of such solution trees? How many “isomorphism classes” are there of trees

T
(
f
)

T(f)

when

f
f

ranges through polynomials of bounded degree and height? We will also give bounds for the number of solutions of congruences

f
(
x
)
≡
0
(
mod

p

λ

)

f(x) \equiv 0 (\text {mod} \,p^{\lambda })

in terms of

p
,
λ

p, \lambda

and the degree of

f
f

.
Isomorphism of lattices of recursively enumerable sets
Authors: Hammond Todd
Published: July 2002

Let

ω
=
{

0
,
1
,
2
,
…

}

\omega = \{\,0,1,2,\ldots \,\}

, and for

A
⊆
ω

A\subseteq \omega

, let

E

A

\mathcal E^A

be the lattice of subsets of

ω
\omega

which are recursively enumerable relative to the “oracle”

A
A

. Let

(

E

A

)
∗

(\mathcal E^A)^*

be

E

A

/

I

\mathcal E^A/\mathcal I

, where

I

\mathcal I

is the ideal of finite subsets of

ω
\omega

. It is established that for any

A
,
B
⊆
ω

A,B\subseteq \omega

,

(

E

A

)
∗

(\mathcal E^A)^*

is effectively isomorphic to

(

E

B

)
∗

(\mathcal E^B)^*

if and only if

A
′

≡
T

B
′

A’\equiv _T B’

, where

A
′

A’

is the Turing jump of

A
A

. A consequence is that if

A
′

≡
T

B
′

A’\equiv _T B’

, then

E

A

≅

E

B

\mathcal E^A\cong \mathcal E^B

. A second consequence is that

(

E

A

)
∗

(\mathcal E^A)^*

can be effectively embedded into

(

E

B

)
∗

(\mathcal E^B)^*

preserving least and greatest elements if and only if

A
′

≤
T

B
′

A’\leq _T B’

.
Coherent functors, with application to torsion in the Picard group
Authors: Jaffe David
Published: July 2002

Let

A
A

be a commutative noetherian ring. We investigate a class of functors from

\lBrack commutative

A
A

-algebras

\rBrack to

\lBrack sets

\rBrack , which we call coherent. When such a functor

F
F

in fact takes its values in

\lBrack abelian groups

\rBrack , we show that there are only finitely many prime numbers

p
p

such that

p

F
(
A
)

{}_pF(A)

is infinite, and that none of these primes are invertible in

A
A

. This (and related statements) yield information about torsion in

Pic
⁡
(
A
)

\operatorname {Pic}(A)

. For example, if

A
A

is of finite type over

Z

\mathbb {Z}

, we prove that the torsion in

Pic
⁡
(
A
)

\operatorname {Pic}(A)

is supported at a finite set of primes, and if

p

Pic
⁡
(
A
)

{}_p\operatorname {Pic}(A)

is infinite, then the prime

p
p

is not invertible in

A
A

. These results use the (already known) fact that if such an

A
A

is normal, then

Pic
⁡
(
A
)

\operatorname {Pic}(A)

is finitely generated. We obtain a parallel result for a reduced scheme

X
X

of finite type over

Z

\mathbb {Z}

. We classify the groups which can occur as the Picard group of a scheme of finite type over a finite field.
The conjugacy problem for groups of alternating prime tame links is polynomial-time
Authors: Johnsgard Karin
Published: July 2002

An alternating projection of a prime link can to used to produce a group presentation (of the link group under free product with the infinite cyclic group) with some useful peculiarities, including small cancellation conditions. In this presentation, conjugacy diagrams are shown to have the form of a tiling of squares in the Euclidean plane in one of a limited number of shapes. An argument based on the shape of the link projection is used to show that the tiling requires no more square tiles than a linear function of word length (with constant multiple based on the number of link crossings). It follows that the computation time for testing conjugacy of two group elements (previously known to be no worse than exponential) is bounded by a cubic polynomial. This bounds complexity in the original link group.
Small cancellation groups and translation numbers
Authors: Kapovich Ilya
Published: July 2002

In this paper we prove that C(4)-T(4)-P, C(3)-T(6)-P and C(6)-P small cancellation groups are translation discrete in the strongest possible sense and that in these groups for any

g
g

and any

n
n

there is an algorithm deciding whether or not the equation

x

n

=
g

x^{n}=g

has a solution. There is also an algorithm for calculating for each

g
g

the maximum

n
n

such that

g
g

is an

n
n

-th power of some element. We also note that these groups cannot contain isomorphic copies of the group of

p
p

-adic fractions and so in particular of the group of rational numbers. Besides we show that for

C

′
′

(
4
)
−
T
(
4
)

C^{\prime \prime }(4)-T(4)

and

C
(
3
)
−
T
(
6
)

C(3)-T(6)

groups all translation numbers are rational and have bounded denominators.
Wavelet transform and orthogonal decomposition of space 𝐿² on the Cartan domain 𝐵𝐷𝐼(𝑞=2)
Authors: Jiang Qingtang
Published: July 2002

Let<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G equals left-parenthesis double-struck upper R Subscript plus Superscript asterisk Baseline times upper S upper O 0 left-parenthesis 1 comma n right-parenthesis right-parenthesis left-normal-factor-semidirect-product double-struck upper R Superscript n plus 1">G=(R+∗×SO0(1,n))⋉Rn+1G=\left ({\mathbb {R}}^{*}_{+}\times SO_{0}(1, n)\right ) \ltimes {\mathbb {R}}^{n+1}be the Weyl-Poincare´\acute egroup andKANKANbe the Iwasawa decomposition ofSO0(1,n)SO_{0}(1, n)withK=SO(n)K=SO(n). Then the “affine Weyl-Poincare´\acute egroup”<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G Subscript a Baseline equals left-parenthesis double-struck upper R Subscript plus Superscript asterisk Baseline times upper A upper N right-parenthesis left-normal-factor-semidirect-product double-struck upper R Superscript n plus 1">Ga=(R+∗×AN)⋉Rn+1G_{a}=\left ({\mathbb {R}}^{*}_{+}\times AN\right ) \ltimes {\mathbb {R}}^{n+1}can be realized as the complex tube domainΠ=Rn+1+iC\Pi ={\mathbb {R}}^{n+1}+iCor the classical Cartan domainBDI(q=2)BDI(q=2). The square-integrable representations ofGGandGaG_{a}give the admissible wavelets and wavelet transforms. An orthogonal basis{ψk}\{ \psi _{k}\}of the set of admissible wavelets associated toGaG_{a}is constructed, and it gives an orthogonal decomposition ofL2L^{2}space onΠ\Pi(or the Cartan domainBDI(q=2)BDI(q=2)) with every componentAkA_{k}being the range of wavelet transforms of functions inH2H^{2}withψk\psi _{k}.
On the Complete Integrability of some Lax Equations on a Periodic Lattice
Authors: Li Luen-Chau
Published: July 2002

We consider some Lax equations on a periodic lattice with

N
=
2

N=2

sites under which the monodromy matrix evolves according to the Toda flows. To establish their integrability (in the sense of Liouville) on generic symplectic leaves of the underlying Poisson structure, we construct the action-angle variables explicitly. The action variables are invariants of certain group actions. In particular, one collection of these invariants is associated with a spectral curve and the linearization of the associated Hamilton equations involves interesting new feature. We also prove the injectivity of the linearization map into real variables and solve the Hamilton equations generated by the invariants via factorization problems.
The stretch of a foliation and geometric superrigidity
Authors: Quiroga-Barranco Raul
Published: July 2002

We consider compact smooth foliated manifolds with leaves isometrically covered by a fixed symmetric space of noncompact type. Such objects can be considered as compact models for the geometry of the symmetric space. Based on this we formulate and solve a geometric superrigidity problem for foliations that seeks the existence of suitable isometric totally geodesic immersions. To achieve this we consider the heat flow equation along the leaves of a foliation, a Bochner formula on foliations and a geometric invariant for foliations with leafwise Riemannian metrics called the stretch. We obtain as applications a metric rigidity theorem for foliations and a rigidity type result for Riemannian manifolds whose geometry is only partially symmetric.
A finiteness theorem for low-codimensional nonsingular subvarieties of quadrics
Authors: de Cataldo Mark
Published: July 2002

We prove that there are only finitely many families of codimension two nonsingular subvarieties of quadrics

Q

n

\mathcal {Q}^{n}

which are not of general type, for

n
=
5

n=5

and

n
≥
7

n\geq 7

. We prove a similar statement also for the case of higher codimension.
Structure of Lorentzian tori with a killing vector field
Authors: Sánchez Miguel
Published: July 2002

All Lorentzian tori with a non-discrete group of isometries are characterized and explicitly obtained. They can lie into three cases: (a) flat, (b) conformally flat but non-flat, and (c) geodesically incomplete. A detailed study of many of their properties (including results on the logical dependence of the three kinds of causal completeness, on geodesic connectedness and on prescribed curvature) is carried out. The incomplete case is specially analyzed, and several known examples and results in the literature are generalized from a unified point of view.
Differential operators on Stanley-Reisner rings
Authors: Tripp J.
Published: July 2002

Let

k
k

be an algebraically closed field of characteristic zero, and let

R
=
k
[

x

1

,
…
,

x

n

]

R=k[x_{1},\dots ,x_{n}]

be a polynomial ring. Suppose that

I
I

is an ideal in

R
R

that may be generated by monomials. We investigate the ring of differential operators

D

(
R

/

I
)

\mathcal {D}(R/I)

on the ring

R

/

I

R/I

, and

I

R

(
I
)

\mathcal {I}_{R}(I)

, the idealiser of

I
I

in

R
R

. We show that

D

(
R

/

I
)

\mathcal {D}(R/I)

and

I

R

(
I
)

\mathcal {I}_{R}(I)

are always right Noetherian rings. If

I
I

is a square-free monomial ideal then we also identify all the two-sided ideals of

I

R

(
I
)

\mathcal {I}_{R}(I)

. To each simplicial complex

Δ
\Delta

on

V
=
{

v

1

,
…
,

v

n

}

V=\{v_{1},\dots ,v_{n}\}

there is a corresponding square-free monomial ideal

I

Δ

I_{\Delta }

, and the Stanley-Reisner ring associated to

Δ
\Delta

is defined to be

k
[
Δ
]
=
R

/

I

Δ

k[\Delta ]=R/I_{\Delta }

. We find necessary and sufficient conditions on

Δ
\Delta

for

D

(
k
[
Δ
]
)

\mathcal {D}(k[\Delta ])

to be left Noetherian.
Bodies with similar projections
Authors: Chakerian G. , Lutwak E.
Published: July 2002

Aleksandrov’s projection theorem characterizes centrally symmetric convex bodies by the measures of their orthogonal projections on lower dimensional subspaces. A general result proved here concerning the mixed volumes of projections of a collection of convex bodies has the following corollary. If

K
K

is a convex body in

R

n

{\mathbb {R}}^{n}

whose projections on

r
r

-dimensional subspaces have the same

r
r

-dimensional volume as the projections of a centrally symmetric convex body

M
M

, then the Quermassintegrals satisfy

W

j

(
M
)
≥

W

j

(
K
)

W_{j}(M)\ge W_{j}(K)

, for

0
≤
j
>
n
−
r

0\le j > n-r

, with equality, for any

j
j

, if and only if

K
K

is a translate of

M
M

. The case where

K
K

is centrally symmetric gives Aleksandrov’s projection theorem.
Extremal properties of Rademacher functions with applications to the Khintchine and Rosenthal inequalities
Authors: Figiel T. , Hitczenko P. , Johnson W. , Schechtman G. , Zinn J.
Published: July 2002

The best constant and the extreme cases in an inequality of H.P. Rosenthal, relating the

p
p

moment of a sum of independent symmetric random variables to that of the

p
p

and

2
2

moments of the individual variables, are computed in the range

2
>
p
≤
4

2>p\le 4

. This complements the work of Utev who has done the same for

p
>
4

p>4

. The qualitative nature of the extreme cases turns out to be different for

p
>
4

p>4

than for

p
>
4

p>4

. The method developed yields results in some more general and other related moment inequalities.
There are no piecewise linear maps of type 2^{∞}
Authors: López Víctor , Snoha L’ubomír
Published: July 2002

The aim of this paper is to show that there are no piecewise linear maps of type2∞2^{\infty }. For this purpose we use the fact that any piecewise monotone map of type2∞2^{\infty }has an infiniteω\omega-limit set which is a subset of a doubling period solenoid. Then we prove that piecewise linear maps cannot have any doubling period solenoids.
Stiefel-Whitney classes and the conormal cycle of a singular variety
Authors: Fu Joseph , McCrory Clint
Published: July 2002

A geometric construction of Sullivan’s Stiefel-Whitney homology classes of a real analytic variety

X
X

is given by means of the conormal cycle of an embedding of

X
X

in a smooth variety. We prove that the Stiefel-Whitney classes define additive natural transformations from certain constructible functions to homology. We also show that, for a complex analytic variety, these classes are the mod 2 reductions of the Chern-MacPherson classes.
Integration of Correspondences on Loeb Spaces
Authors: Sun Yeneng
Published: July 2002

We study the Bochner and Gel

′

^{\prime }

fand integration of Banach space valued correspondences on a general Loeb space. Though it is well known that the Lyapunov type result on the compactness and convexity of the integral of a correspondence and the Fatou type result on the preservation of upper semicontinuity by integration are in general not valid in the setting of an infinite dimensional space, we show that exact versions of these two results hold in the case we study. We also note that our results on a hyperfinite Loeb space capture the nature of the corresponding asymptotic results for the large finite case; but the unit Lebesgue interval fails to provide such a framework.
The generalized Berg theorem and BDF-theorem
Authors: Lin Huaxin
Published: July 2002

Let

A
A

be a separable simple

A
F

AF

-algebra with finitely many extreme traces. We give a necessary and sufficient condition for an essentially normal element

x
∈
M
(
A
)

x\in M(A)

, i.e.,

π
(
x
)

\pi (x)

is normal (

π
:
M
(
A
)
→
M
(
A
)

/

A

\pi : M(A)\to M(A)/A

is the quotient map), having the form

y
+
a

y+a

for some normal element

y
∈
M
(
A
)

y\in M(A)

and

a
∈
A
.

a\in A.

We also show that a normal element

x
∈
M
(
A
)

x\in M(A)

can be quasi-diagonalized if and only if the Fredholm index

i
n
d
(
λ
−
x
)
=
0

ind(\lambda -x)=0

for all

λ
∉
s
p
(
π
(
x
)
)
.

\lambda \not \in sp(\pi (x)).

In the case that

A
A

is a simple

C
∗

C^*

-algebra  of real rank zero, with stable rank one and with continuous scale,

K
1

(
A
)
=
0
,

K_1(A)=0,

and

K
0

(
A
)

K_0(A)

has countable rank, we show that a normal element

x
∈
M
(
A
)

x\in M(A)

with zero Fredholm index can be written as

x
=

∑

n
=
1

∞

λ
n

(

e
n

−

e

n
−
1

)
+
a
,

\begin{equation*} x=\sum _{n=1}^{\infty }\lambda _n(e_n-e_{n-1})+a, \end{equation*}

where

{

e
n

}

\{e_n\}

is an (increasing) approximate identity for

A
A

consisting of projections,

{

λ
n

}

\{\lambda _n\}

is a bounded sequence of numbers and

a
∈
A

a\in A

with

‖
a
‖
>
ϵ

\|a\|>\epsilon

for any given

ϵ
>
0.

\epsilon >0.
Randomness and semigenericity
Authors: Baldwin John , Shelah Saharon
Published: July 2002

LetLLcontain only the equality symbol and letL+L^+be an arbitrary finite symmetric relational language containingLL. Suppose probabilities are defined on finiteL+L^+structures with ‘edge probability’n−αn^{-\alpha }. ByTαT^{\alpha }, the almost sure theory of randomL+L^+-structures we mean the collection ofL+L^+-sentences which have limit probability 1.TαT_{\alpha }denotes the theory of the generic structures forKα\mathbb {K}_{\alpha }(the collection of finite graphsGGwithδα(G)=|G|−α⋅|edges of G|\delta _\alpha (G) = |G| - \alpha \cdot |\text {edges of $G$}|hereditarily nonnegative).

Theorem.TαT^{\alpha }, the almost sure theory of randomL+L^+-structures, is the same as the theoryTαT_{\alpha }of theKα\mathbb {K}_{\alpha }-generic model. This theory is complete, stable, and nearly model complete. Moreover, it has the finite model property and has only infinite models so is not finitely axiomatizable.
Covering Sato-Levine invariants
Authors: Li Gui-Song
Published: July 2002

Two covering versions of the Sato-Levine invariant are constructed which provide obstructions to certain two-component oriented links in the 3-sphere being link concordant to boundary links. These covering invariants are rational functions one of which detects both nonamphicheirality and noninvertibility of oriented links.
Duality of restriction and induction for 𝐶*-coactions
Authors: Kaliszewski S. , Quigg John , Raeburn Iain
Published: July 2002

Consider a coaction

δ
\delta

of a locally compact group

G
G

on a

C
∗

C^*

algebra

A
A

, and a closed normal subgroup

N
N

of

G
G

. We prove, following results of Echterhoff for abelian

G
G

, that Mansfield’s imprimitivity between

A

×

δ

|

G

/

N

A\times _{\delta |}G/N

and

A

×
δ

G

×

δ
^

,
r

N

A\times _\delta G\times _{\hat \delta ,r}N

implements equivalences between Mansfield induction of representations from

A

×

δ

|

G

/

N

A\times _{\delta |}G/N

to

A

×
δ

G

A\times _\delta G

and restriction of representations from

A

×
δ

G

×

δ
^

,
r

N

A\times _\delta G\times _{\hat \delta ,r}N

to

A

×
δ

G

A\times _\delta G

, and between restriction of representations from

A

×
δ

G

A\times _\delta G

to

A

×

δ

|

G

/

N

A\times _{\delta |}G/N

and Green induction of representations from

A

×
δ

G

A\times _\delta G

to

A

×
δ

G

×

δ
^

,
r

N

A\times _\delta G\times _{\hat \delta ,r}N

. This allows us to deduce properties of Mansfield induction from the known theory of ordinary crossed products.
On singly-periodic minimal surfaces with planar ends
Authors: Pérez Joaquín
Published: July 2002

The spaces of nondegenerate properly embedded minimal surfaces in quotients of

R

3

{\mathbf R}^3

by nontrivial translations or by screw motions with nontrivial rotational part, fixed finite topology and planar type ends, are endowed with natural structures of finite dimensional real analytic manifolds. This nondegeneracy is defined in terms of Jacobi functions. Riemann’s minimal examples are characterized as the only nondegenerate surfaces with genus one in their corresponding spaces. We also give natural immersions of these spaces into certain complex Euclidean spaces which turn out to be Lagrangian immersions with respect to the standard symplectic structures.