bluuebunny/crossref_metadata_2025_split huggingface dataset:
On Amenability and Co-Amenability of Algebraic Quantum Groups and Their Corepresentations
Authors: Bédos Erik , Conti Roberto , Tuset Lars 
Published: December 2010

AbstractWe introduce and study several notions of amenability for unitary corepresentations and *-representations of algebraic quantum groups, which may be used to characterize amenability and co-amenability for such quantumgroups. As a background for this study, we investigate the associated tensor C*-categories.
On the Waring–Goldbach Problem: Exceptional Sets for Sums of Cubes and Higher Powers
Authors: Kumchev Angel V. 
Published: December 2010

AbstractWe investigate exceptional sets in theWaring–Goldbach problem. For example, in the cubic case, we show that all but O(N79/84+∊) integers subject to the necessary local conditions can be represented as the sum of five cubes of primes. Furthermore, we develop a new device that leads easily to similar estimates for exceptional sets for sums of fourth and higher powers of primes.
Generalized k-Configurations
Authors: Sabourin Sindi 
Published: December 2010

AbstractIn this paper, we find configurations of points in n-dimensional projective space (Pn) which simultaneously generalize both k-configurations and reduced 0-dimensional complete intersections. Recall that k-configurations in P2 are disjoint unions of distinct points on lines and in Pn are inductively disjoint unions of k-configurations on hyperplanes, subject to certain conditions. Furthermore, the Hilbert function of a k-configuration is determined from those of the smaller k-configurations. We call our generalized constructions kD-configurations, where D = {d1, … , dr} (a set of r positive integers with repetition allowed) is the type of a given complete intersection in Pn. We show that the Hilbert function of any kD-configuration can be obtained from those of smaller kD-configurations. We then provide applications of this result in two different directions, both of which are motivated by corresponding results about k-configurations.
On the Sizes of Gaps in the Fourier Expansion of Modular Forms
Authors: Alkan Emre 
Published: December 2010

AbstractLet be a cusp form with integer weight k ≥ 2 that is not a linear combination of forms with complex multiplication. For n ≥ 1, letConcerning bounded values of i f (n) we prove that for ∊ > 0 there exists M = M(∊, f ) such that Using results of Wu, we show that if f is a weight 2 cusp form for an elliptic curve without complex multiplication, then . Using a result of David and Pappalardi, we improve the exponent to for almost all newforms associated to elliptic curves without complex multiplication. Inspired by a classical paper of Selberg, we also investigate i f (n) on the average using well known bounds on the Riemann Zeta function.
Reverse Hypercontractivity for Subharmonic Functions
Authors: Gross Leonard , Grothaus Martin 
Published: December 2010

AbstractContractivity and hypercontractivity properties of semigroups are now well understood when the generator, A, is a Dirichlet form operator. It has been shown that in some holomorphic function spaces the semigroup operators, e−tA, can be bounded below from Lp to Lq when p, q and t are suitably related. We will show that such lower boundedness occurs also in spaces of subharmonic functions.
Branching Rules for Principal Series Representations of SL(2) over a p-adic Field
Authors: Nevins Monica 
Published: December 2010

AbstractWe explicitly describe the decomposition into irreducibles of the restriction of the principal series representations of SL(2, k), for k a p-adic field, to each of its two maximal compact subgroups (up to conjugacy). We identify these irreducible subrepresentations in the Kirillov-type classification of Shalika. We go on to explicitly describe the decomposition of the reducible principal series of SL(2, k) in terms of the restrictions of its irreducible constituents to a maximal compact subgroup.
Curvature Estimates in Asymptotically Flat Lorentzian Manifolds
Authors: Finster Felix , Kraus Margarita 
Published: December 2010

AbstractWe consider an asymptotically flat Lorentzian manifold of dimension (1, 3). An inequality is derived which bounds the Riemannian curvature tensor in terms of the ADM energy in the general case with second fundamental form. The inequality quantifies in which sense the Lorentzianmanifold becomes flat in the limit when the ADM energy tends to zero.
Representation of Banach Ideal Spaces and Factorization of Operators
Authors: Berezhnoĭ Evgenii I. , Maligranda Lech 
Published: December 2010

AbstractRepresentation theorems are proved for Banach ideal spaces with the Fatou property which are built by the Calderón–Lozanovskiĭ construction. Factorization theorems for operators in spaces more general than the Lebesgue Lpspaces are investigated. It is natural to extend the Gagliardo theorem on the Schur test and the Rubio de Francia theorem on factorization of the Muckenhoupt Ap weights to reflexive Orlicz spaces. However, it turns out that for the scales far fromLp-spaces this is impossible. For the concrete integral operators it is shown that factorization theorems and the Schur test in some reflexive Orlicz spaces are not valid. Representation theorems for the Calderón–Lozanovskiĭ construction are involved in the proofs.
Some Transformations of Hausdorff Moment Sequences and Harmonic Numbers
Authors: Berg Christian , Durán Antonio J. 
Published: December 2010

AbstractWe introduce some non-linear transformations from the set of Hausdorff moment sequences into itself; among them is the one defined by the formula: . We give some examples of Hausdorff moment sequences arising from the transformations and provide the corresponding measures: one of these sequences is the reciprocal of the harmonic numbers .
Cone-Monotone Functions: Differentiability and Continuity
Authors: Borwein Jonathan M. , Wang Xianfu 
Published: December 2010

AbstractWe provide a porosity-based approach to the differentiability and continuity of real-valued functions on separable Banach spaces, when the function is monotone with respect to an ordering induced by a convex cone K with non-empty interior. We also show that the set of nowhere K-monotone functions has a σ-porous complement in the space of continuous functions endowed with the uniform metric.
Constructing Representations of Finite Simple Groups and Covers
Authors: Dabbaghian-Abdoly Vahid 
Published: December 2010

AbstractLet G be a finite group and χ be an irreducible character of G. An efficient and simple method to construct representations of finite groups is applicable whenever G has a subgroup H such that χH has a linear constituent with multiplicity 1. In this paper we show (with a few exceptions) that if G is a simple group or a covering group of a simple group and χ is an irreducible character of G of degree less than 32, then there exists a subgroup H (often a Sylow subgroup) of G such that χH has a linear constituent with multiplicity 1.
Quelques résultats sur les équations axp + byp = cz2
Authors: Ivorra W. , Kraus A. 
Published: December 2010

AbstractLet p be a prime number ≥ 5 and a, b, c be non zero natural numbers. Using the works of K. Ribet and A. Wiles on the modular representations, we get new results about the description of the primitive solutions of the diophantine equation axp + byp = cz2, in case the product of the prime divisors of abc divides 2ℓ, with ℓ an odd prime number. For instance, under some conditions on a, b, c, we provide a constant f (a, b, c) such that there are no such solutions if p > f (a, b, c). In application, we obtain information concerning the ℚ-rational points of hyperelliptic curves given by the equation y2 = xp + d with d ∈ ℤ.
Convergence of Fourier–Padé Approximants for Stieltjes Functions
Authors: Bello Hernández M. , Mínguez Ceniceros J. 
Published: December 2010

AbstractWe prove convergence of diagonal multipoint Padé approximants of Stieltjes-type functions when a certain moment problem is determinate. This is used for the study of the convergence of Fourier–Padé and nonlinear Fourier–Padé approximants for such type of functions.
Non-reductive Homogeneous Pseudo-Riemannian Manifolds of Dimension Four
Authors: Fels M. E. , Renner A. G. 
Published: December 2010

AbstractA method, due to Élie Cartan, is used to give an algebraic classification of the non-reductive homogeneous pseudo-Riemannian manifolds of dimension four. Only one case with Lorentz signature can be Einstein without having constant curvature, and two cases with (2, 2) signature are Einstein of which one is Ricci-flat. If a four-dimensional non-reductive homogeneous pseudo-Riemannian manifold is simply connected, then it is shown to be diffeomorphic to ℝ4. All metrics for the simply connected non-reductive Einstein spaces are given explicitly. There are no non-reductive pseudo-Riemannian homogeneous spaces of dimension two and none of dimension three with connected isotropy subgroup.
Reducibility for SUn and Generic Elliptic Representations
Authors: Goldberg David 
Published: December 2010

AbstractWe study reducibility of representations parabolically induced from discrete series representations of SUn(F) for F a p-adic field of characteristic zero. We use the approach of studying the relation between R-groups when a reductive subgroup of a quasi-split group and the full group have the same derived group. We use restriction to show the quotient of R-groups is in natural bijection with a group of characters. Applying this to SUn(F) ⊂ Un(F) we show the R group for SUn is the semidirect product of an R-group for Un(F) and this group of characters. We derive results on nonabelian R-groups and generic elliptic representations as well.
Geometric Study of Minkowski Differences of Plane Convex Bodies
Authors: Martinez-Maure Yves 
Published: December 2010

AbstractIn the Euclidean plane ℝ2, we define the Minkowski difference 𝒦–𝓛 of two arbitrary convex bodies 𝒦, 𝓛 as a rectifiable closed curve ℋh⊂ ℝ2that is determined by the differenceh=h𝒦–h𝓛of their support functions. This curve ℋhis called the hedgehog with support functionh. More generally, the object of hedgehog theory is to study the Brunn–Minkowski theory in the vector space of Minkowski differences of arbitrary convex bodies of Euclidean space ℝn+1, defined as (possibly singular and self-intersecting) hypersurfaces of ℝn+1. Hedgehog theory is useful for: (i) studying convex bodies by splitting them into a sum in order to reveal their structure; (ii) converting analytical problems into geometrical ones by considering certain real functions as support functions. The purpose of this paper is to give a detailed study of plane hedgehogs, which constitute the basis of the theory. In particular: (i) we study their lengthmeasures and solve the extension of the Christoffel–Minkowski problemto plane hedgehogs; (ii) we characterize support functions of plane convex bodies among support functions of plane hedgehogs and support functions of plane hedgehogs among continuous functions; (iii) we study the mixed area of hedgehogs in ℝ2and give an extension of the classical Minkowski inequality (and thus of the isoperimetric inequality) to hedgehogs.
A Steinberg Cross Section for Non–Connected Affine Kac—Moody Groups
Authors: Mohrdieck Stephan 
Published: December 2010

AbstractIn this paper we generalise the concept of a Steinberg cross section to non–connected affine Kac–Moody groups. This Steinberg cross section is a section to the restriction of the adjoint quotient map to a given exterior connected component of the affine Kac–Moody group. (The adjoint quotient is only defined on a certain submonoid of the entire group, however, the intersection of this submonoid with each connected component is non-void.) The image of the Steinberg cross section consists of a “twisted Coxeter cell”, a transversal slice to a twisted Coxeter element. A crucial point in the proof of the main result is that the image of the cross section can be endowed with a 𝕔*-action.
The Generalized Cuspidal Cohomology Problem
Authors: Bart Anneke , Scannell Kevin P. 
Published: December 2010

AbstractLet Γ ⊂ SO(3, 1) be a lattice. The well known bending deformations, introduced by Thurston and Apanasov, can be used to construct non-trivial curves of representations of Γ into SO(4, 1) when Γ\ℍ3 contains an embedded totally geodesic surface. A tangent vector to such a curve is given by a non-zero group cohomology class in H1(Γ, ℍ41). Our main result generalizes this construction of cohomology to the context of “branched” totally geodesic surfaces. We also consider a natural generalization of the famous cuspidal cohomology problem for the Bianchi groups (to coefficients in non-trivial representations), and perform calculations in a finite range. These calculations lead directly to an interesting example of a link complement in S3 which is not infinitesimally rigid in SO(4, 1). The first order deformations of this link complement are supported on a piecewise totally geodesic 2-complex.
Nonstandard Ideals from Nonstandard Dual Pairs for L1(ω) and l1(ω)
Authors: Read C. J. 
Published: December 2010

AbstractThe Banach convolution algebras l1(ω) and their continuous counterparts L1(ℝ+, ω) are much studied, because (when the submultiplicative weight function ω is radical) they are pretty much the prototypic examples of commutative radical Banach algebras. In cases of “nice” weights ω, the only closed ideals they have are the obvious, or “standard”, ideals. But in the general case, a brilliant but very difficult paper of Marc Thomas shows that nonstandard ideals exist in l1(ω). His proof was successfully exported to the continuous case L1(ℝ+, ω) by Dales and McClure, but remained difficult. In this paper we first present a small improvement: a new and easier proof of the existence of nonstandard ideals in l1(ω) and L1(ℝ+, ω). The new proof is based on the idea of a “nonstandard dual pair” which we introduce. We are then able to make a much larger improvement: we find nonstandard ideals in L1(ℝ+, ω) containing functions whose supports extend all the way down to zero in ℝ+, thereby solving what has become a notorious problem in the area.
Karamata Renewed and Local Limit Results
Authors: Handelman David 
Published: December 2010

AbstractConnections between behaviour of real analytic functions (with no negative Maclaurin series coefficients and radius of convergence one) on the open unit interval, and to a lesser extent on arcs of the unit circle, are explored, beginning with Karamata's approach. We develop conditions under which the asymptotics of the coefficients are related to the values of the function near 1; specifically, a(n) ∼ f(1 – 1/n)/αn (for some positive constant α), where f(t) = Σa(n)tn. In particular, if F = Σc(n)tn where c(n) ≥ 0 and Σc(n) = 1, then f defined as (1 – F)–1 (the renewal or Green's function for F) satisfies this condition if F′ does (and a minor additional condition is satisfied). In come cases, we can show that the absolute sum of the differences of consecutiveMaclaurin coefficients converges. We also investigate situations in which less precise asymptotics are available.
Gauge-Invariant Ideals in theC*-Algebras of Finitely Aligned Higher-Rank Graphs
Authors: Sims Aidan 
Published: December 2010

AbstractWe produce a complete description of the lattice of gauge-invariant ideals inC*(Λ) for a finitely alignedk-graph Λ. We provide a condition on Λ under which every ideal is gauge-invariant. We give conditions on Λ under whichC*(Λ) satisfies the hypotheses of the Kirchberg–Phillips classification theorem.
Classification of Ding's Schubert Varieties: Finer Rook Equivalence
Authors: Develin Mike , Martin Jeremy L. , Reiner Victor 
Published: December 2010

AbstractK. Ding studied a class of Schubert varieties Xƛ in type A partial flag manifolds, indexed by integer partitions ƛ and in bijection with dominant permutations. He observed that the Schubert cell structure of Xƛ is indexed by maximal rook placements on the Ferrers board Bƛ, and that the integral cohomology groups H*(Xƛ; ℤ), H*(Xμ; ℤ) are additively isomorphic exactly when the Ferrers boards Bƛ, Bμ satisfy the combinatorial condition of rook-equivalence.We classify the varieties Xƛ up to isomorphism, distinguishing them by their graded cohomology rings with integer coefficients. The crux of our approach is studying the nilpotence orders of linear forms in the cohomology ring.
Endomorphism Algebras of Kronecker Modules Regulated by Quadratic Function Fields
Authors: Okoh F. , Zorzitto F. 
Published: December 2010

AbstractPurely simple Kronecker modules ℳ, built from an algebraically closed field K, arise from a triplet (m, h, α) where m is a positive integer, h: K ∪ ﹛∞﹜ → ﹛∞, 0, 1, 2, 3, … ﹜ is a height function, and α is a K-linear functional on the space K(X) of rational functions in one variable X. Every pair (h, α) comes with a polynomial f in K(X)[Y] called the regulator. When the module ℳ admits nontrivial endomorphisms, f must be linear or quadratic in Y. In that case ℳ is purely simple if and only if f is an irreducible quadratic. Then the K-algebra End ℳ embeds in the quadratic function field K(X)[Y]/(f). For some height functions h of infinite support I, the search for a functional α for which (h, α) has regulator 0 comes down to having functions η : I → K such that no planar curve intersects the graph of η on a cofinite subset. If K has characterictic not 2, and the triplet (m, h, α) gives a purely-simple Kronecker module ℳ having non-trivial endomorphisms, then h attains the value ∞ at least once on K ∪ ﹛∞﹜ and h is finite-valued at least twice on K ∪ ﹛∞﹜. Conversely all these h form part of such triplets. The proof of this result hinges on the fact that a rational function r is a perfect square in K(X) if and only if r is a perfect square in the completions of K(X) with respect to all of its valuations.
Weak Semiprojectivity in Purely Infinite SimpleC*-Algebras
Authors: Lin Huaxin 
Published: December 2010

AbstractLetAbe a separable amenable purely infinite simpleC*-algebra which satisfies the Universal Coefficient Theorem. We prove thatAis weakly semiprojective if and only ifKi(A) is a countable direct sum of finitely generated groups (i= 0, 1). Therefore, ifAis such aC*-algebra, for any ε > 0 and any finite subset ℱ ⊂Athere existδ> 0 and a finite subset⊂Asatisfying the following: for any contractive positive linear mapL:A→B(for anyC*-algebraB) with ∥L(ab) –L(a)L(b)∥ <δfora,b∈there exists a homomorphismh:A→Bsuch that ∥h(a) –L(a)∥ < ε fora∈ ℱ.
Distance from Idempotents to Nilpotents
Authors: MacDonald Gordon W. 
Published: December 2010

AbstractWe give bounds on the distance from a non-zero idempotent to the set of nilpotents in the set of n × n matrices in terms of the norm of the idempotent. We construct explicit idempotents and nilpotents which achieve these distances, and determine exact distances in some special cases.
Algèbres de Lie d'homotopie associées à une proto-bigèbre de Lie
Authors: Bangoura Momo 
Published: December 2010

RésuméOn associe à toute structure de proto-bigèbre de Lie sur un espace vectoriel F de dimension finie des structures d’algèbre de Lie d’homotopie définies respectivement sur la suspension de l’algèbre extérieure de F et celle de son dual F*. Dans ces algèbres, tous les crochets n-aires sont nuls pour n ≥ 4 du fait qu’ils proviennent d’une structure de proto-bigèbre de Lie. Plus généralement, on associe à un élément de degré impair de l’algèbre extérieure de la somme directe de F et F*, une collection d’applications multilinéaires antisymétriques sur l’algèbre extérieure de F (resp. F*), qui vérifient les identités de Jacobi généralisées, définissant les algèbres de Lie d’homotopie, si l’élément donné est de carré nul pour le grand crochet de l’algèbre extérieure de la somme directe de F et de F*.
Representations of the Fundamental Group of an L–Punctured Sphere Generated by Products of Lagrangian Involutions
Authors: Schaffhauser Florent 
Published: December 2010

AbstractIn this paper, we characterize unitary representations of π := π1(S2\{s1, … , sl}) whose generators u1, … , ul (lying in conjugacy classes fixed initially) can be decomposed as products of two Lagrangian involutions uj = σjσj+1 with σl+1 = σ1. Our main result is that such representations are exactly the elements of the fixed-point set of an anti-symplectic involution defined on the moduli space ℳᘓ := Homᘓ(π, U(n))/U(n). Consequently, as this fixed-point set is non-empty, it is a Lagrangian submanifold of ℳᘓ. To prove this, we use the quasi-Hamiltonian description of the symplectic structure of ℳᘓ and give conditions on an involution defined on a quasi-Hamiltonian U-space (M, ω, μ: M → U) for it to induce an anti-symplectic involution on the reduced space M//U := μ–1({1})/U.
Admissibility for a Class of Quasiregular Representations
Authors: Currey Bradley N. 
Published: December 2010

AbstractGiven a semidirect product G = N ⋊ H where N is nilpotent, connected, simply connected and normal in G and where H is a vector group for which ad() is completely reducible and R-split, let τ denote the quasiregular representation of G in L2(N). An element ψ ∈ L2(N) is said to be admissible if the wavelet transform f ⟼ 〈 f, τ(·)ψ 〉 defines an isometry from L2(N) into L2(G). In this paper we give an explicit construction of admissible vectors in the case where G is not unimodular and the stabilizers in H of its action on are almost everywhere trivial. In this situation we prove orthogonality relations and we construct an explicit decomposition of L2(G) into G-invariant, multiplicity-free subspaces each of which is the image of a wavelet transform . We also show that, with the assumption of (almost-everywhere) trivial stabilizers, non-unimodularity is necessary for the existence of admissible vectors.
The Chen–Ruan Cohomology of Weighted Projective Spaces
Authors: Jiang Yunfeng 
Published: December 2010

AbstractIn this paper we study the Chen–Ruan cohomology ring of weighted projective spaces. Given a weighted projective space we determine all of its twisted sectors and the corresponding degree shifting numbers. The main result of this paper is that the obstruction bundle over any 3-multisector is a direct sum of line bundles which we use to compute the orbifold cup product. Finally we compute the Chen–Ruan cohomology ring of weighted projective space
Ruled Exceptional Surfaces and the Poles of Motivic Zeta Functions
Authors: Rodrigues B. 
Published: December 2010

AbstractIn this paper we study ruled surfaces which appear as exceptional surface in a succession of blowing-ups. In particular we prove that the e-invariant of such a ruled exceptional surface E is strictly positive whenever its intersection with the other exceptional surfaces does not contain a fiber (of E). This fact immediately enables us to resolve an open problem concerning an intersection configuration on such a ruled exceptional surface consisting of three nonintersecting sections. In the second part of the paper we apply the non-vanishing of e to the study of the poles of the well-known topological, Hodge and motivic zeta functions.
k(n)-Torsion-Free H-Spaces and P(n)-Cohomology
Authors: Michael Boardman J. , Stephen Wilson W. 
Published: December 2010

AbstractThe H-space that represents Brown–Peterson cohomology BPk(–) was split by the second author into indecomposable factors, which all have torsion-free homotopy and homology. Here, we do the same for the related spectrum P(n), by constructing idempotent operations in P(n)–cohomology P(n)k(–) in the style of Boardman–Johnson–Wilson; this relies heavily on the Ravenel–Wilson determination of the relevant Hopf ring. The resulting (i – 1)-connected H-spaces Yi have free connective Morava K-homology k(n)*(Yi), and may be built from the spaces in the Ω-spectrum for k(n) using only vn-torsion invariants.We also extend Quillen's theorem on complex cobordism to show that for any space X, the P(n)*-module P(n)*(X) is generated by elements of P(n)i(X) for i ≥ 0. This result is essential for the work of Ravenel–Wilson–Yagita, which in many cases allows one to compute BP–cohomology from Morava K-theory.