Twisted Semigroup Crossed Products and Twisted Toeplitz Algebras of Ordered Groups

Let г^＋ be the positive cone of a totally ordered abelian group г, and σa cocycle in г. We study the twisted crossed products by actions of г＋ as endomorphisms of C^＊-algebras, and use this to generalize the theorem of Ji.     

Ideals and Representations of Certain Semigroup Algebras

We characterize various types of ideals in ¹-Munn algebras with a bounded approximate identity, in terms of the ideals of their underlying algebras. Moreover, we show the correspondence between different types of *-representations of ¹-Munn algebras and *-representations of their underlying algebras. In the context of semigroup algebras, .rst we prove the conjecture which was proposed in [8]. Then we apply the results of the first part to build various representations of unital semigroup algebras of completely 0-simple inverse semigroups. This generalizes some of the Barnes results [1] with different and much shorter proofs.     

Parabolically Induced Representations of Graded Hecke Algebras

We study the representation theory of graded Hecke algebras, starting from scratch and focusing on representations that are obtained by induction from a discrete series representation of a parabolic subalgebra. We determine all intertwining operators between such parabolically induced representations, and use them to parametrize the irreducible representations. Finally we describe the spectrum of a graded Hecke algebra as a topological space.     

Semisimple Representations of Alternating Cyclotomic Hecke Algebras

We define alternating cyclotomic Hecke algebras in higher levels as subalgebras of cyclotomic Hecke algebras under an analogue of Goldman’s hash involution. We compute the rank of these algebras and construct a full set of irreducible representations in the semisimple case, generalising Mitsuhashi’s results Mitsuhashi (J. Alg. 240 535–558 2001, J. Alg. 264 231–250 2003).     

Representations and Corresponding Operators Induced by Hecke Algebras

In this paper, by establishing free-probabilistic models on the Hecke algebras \(\mathcal {H}(G_{p})\), we construct canonical free probability spaces \((\mathcal {H}(G_{p}), \psi _{p})\), where \(G_{p} = GL_{2}(\mathbb {Q} _{p})\), for primes \(p\). Dependent upon such free-probabilistic structures, we study corresponding representations of \(\mathcal {H}(G_{p})\), and consider spectral properties of operators realized under representations.     

The Classification of Representations f Unramified Hecke Algebras

We give two characterizations of the isolated singularities of the local resolvent function of an operator T ε L(X) at a point ε of a complex Banach space X: in terms of a suitable decomposition of ε, and in terms of the existence of a sequence in X related with the Laurent series of the local resolvent function. Moreover, we introduce the locally chain-finite operators at a point ε and show that T is chain-finite if and only if T is locally chain-finite at every χ ε X.     

On Representations of Affine Hecke Algebras of Type B

Ariki’s and Grojnowski’s approach to the representation theory of affine Hecke algebras of type A is applied to type B with unequal parameters to obtain – under certain restrictions on the eigenvalues of the lattice operators – analogous multiplicity-one results and a classification of irreducibles with partial branching rules as in type A. Research supported by the Studienstiftung des deutschen Volkes.     

Crossed Products for Weak Hopf Algebras

Weak crossed products by a weak bialgebra are defined. The resulting structure is not that of a unital algebra but an associative algebra with preunit. A general formula of such a product is given in terms of a weak 2-cocycle and a weak measuring. The relation with weak cleft extensions is studied. Equivalences of weak crossed products are defined and are related to gauge transformations. A relation between cleaving maps is described in terms of gauge transformations.     

Representations of Reductive p-Adic Groups: Localization of Hecke Algebras and Applications

Let F be a non-Archimedean local field and G be the group ofF-points of a connected reductive group defined over F. LetM be an F-Levi subgroup of G and P = MN be a parabolic subgroupwith Levi decomposition P = MN. Jacquet, or truncated, restrictiongives a functor from the category of smooth representationsof G to that of M. The main result describes this functor interms of homomorphisms and localizations of Hecke algebras attachedto certain compact open subgroups of G and M. This leads tonew and straightforward proofs of some fundamental results.The first computes the smooth dual of a Jacquet module of asmooth representation of G, generalizing the corresponding resultfor admissible representations due to Harish-Chandra and Casselman.The second identifies the co-adjoint of the Jacquet functorrelative to P as the induction functor relative to the M-oppositeof P, an unpublished result of J.-N. Bernstein.     

On Weak Crossed Products of Weak Hopf Algebras

Let H be a weak Hopf algebra in the sense of Böhm et al. (J Algebra 221:385–438, 1999) measuring an algebra A. Let A# _σ H be a weak crossed product with σ invertible. Then in this paper we first give some conditions for A# _σ H to be a weak Hopf algebra. Next the spectral sequence for Ext will be constructed which yields an estimate for the global dimension of A# _σ H in terms of the corresponding data for H and A. Furthermore, we will investigate when A???A# _σ H becomes a separable extension. Finally, we prove that if H and its dual H* are both semisimple, then the finitistic dimension of A# _σ H is equal to that of A.     

Hopf代数交叉积的同调维数

Let H be a finite dimensional cocommutative Hopf algebra and A an H-module algebra, ln this paper, we characterize the projectivity (injectivity) of M as a left A#σ H-module when it is projective (injective) as a left A-module. The sufficient and necessary condition for A#σ H, the crossed product, to have finite global homological dimension is given, in terms of the global homological dimension of A and the surjectivity of trace maps, provided that H is cocommutative and A is commutative.     

弱Hopf代数上的对角交叉积和左右冲积(英文)

作为弱Hopf代数上的冲积的推广,本文引入了弱Hopf代数上的对角交叉积和左右冲积概念,并研究了它们的性质.特别地,有限维弱Hopf代数上的Drinfeld对是一种特殊的对角交叉积,本文给出了其上的弱Hopf代数结构.作为两个典型的例子,本文引入并研究了弱Hopf代数上Kadison积和Connes-Moscovici积.     

A Note on Regular Crossed Products and Galois Representations

A crossed product representing an associative finite dimensional central simple algebra over a field is called regular if all values of the corresponding cocycle are roots of unity. Under a certain assumption such a crossed product is shown to allow the construction of Galois representations. The case of number fields is investigated more closely and several examples are discussed.     

Topologically Free Partial Actions and Faithful Representations of Crossed Products

We study the relationship between the topological freeness of partial actions of discrete groups and faithful representations of the corresponding crossed products.     

Hecke Algebras and SLn-Types

Let F be a non-Archimedean local field. In an earlier paper,we constructed certain types (in the sense of Bushnell and Kutzko)in SL_n (F), in fact enough to describe the non-supercuspidalcomponents of the Bernstein decomposition of this group. Wenow give an almost fully explicit presentation of the Heckealgebras of these types. 2000 Mathematics Subject Classification22E50, 20G05.     

von Neumann代数交叉积的注记

设A是B(H)中的极大交换*-子代数, G是离散群,在不要求G自由地作用在A的情况下,得到了交叉积A×αG是因子的充分且必要条件.     

Noetherian Semigroup Algebras

A complete structural characterization of submonoids S of apolycyclic-by-finite group such that the semigroup algebra K[S]over a field K is right noetherian is obtained. It follows thatsuch algebras are also left noetherian. 2000 Mathematics SubjectClassification 16P40, 16S36, 20M25 (primary), 20F22, 20C07,20M10 (secondary).