共查询到20条相似文献,搜索用时 15 毫秒
1.
高楠 《数学物理学报(B辑英文版)》2008,28(4):870-876
This article is devoted to the study of the symmetry in the Yetter-Drinfeld category of a finite-dimensional weak Hopf algebra.It generalizes the corresponding results in Hopf algebras. 相似文献
2.
Let 𝒜 be a commutative unital algebra over an algebraically closed field k of characteristic ≠2, whose generators form a finite-dimensional subspace V, with no nontrivial homogeneous quadratic relations. Let 𝒬 be a Hopf algebra that coacts on 𝒜 inner-faithfully, while leaving V invariant. We prove that 𝒬 must be commutative when either: (i) the coaction preserves a non-degenerate bilinear form on V; or (ii) 𝒬 is co-semisimple, finite-dimensional, and char(k) = 0. 相似文献
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4.
RunQiang Jian 《中国科学 数学(英文版)》2014,57(11):2321-2328
We propose the notion of Hopf module algebra and show that the projection onto the subspace of coinvariants is an idempotent Rota-Baxter operator of weight-1. We also provide a construction of Hopf module algebras by using Yetter-Drinfeld module algebras. As an application,we prove that the positive part of a quantum group admits idempotent Rota-Baxter algebra structures. 相似文献
5.
In this paper, we first give a sufficient and necessary condition for a Hopf algebra to be a Yetter-Drinfel'd module, and prove that the finite dual of a Yetter-Drinfel'd module is still a Yetter-Drinfel'd module. Finally, we introduce a concept of convolution module. 相似文献
6.
DENG Bangming 《中国科学A辑(英文版)》2000,43(11)
This paper gives a complete classification of F (Δ)-finite twisted double incidence algebras of posets in the case where the Hasse quivers of posets are of type An. 相似文献
7.
Let B→A be a homomorphism of Hopf algebras and let C be an algebra. We consider the induction from B to A of C in two cases: when C is a B-interior algebra and when C is a B-module algebra. Our main results establish the connection between the two inductions. The inspiration comes from finite group representation theory, and some constructions work in even more general contexts. 相似文献
8.
Becky Armstrong Lisa Orloff Clark Kristin Courtney Ying-Fen Lin Kathryn McCormick Jacqui Ramagge 《Journal of Pure and Applied Algebra》2022,226(3):106853
We introduce twisted Steinberg algebras over a commutative unital ring R. These generalise Steinberg algebras and are a purely algebraic analogue of Renault's twisted groupoid C*-algebras. In particular, for each ample Hausdorff groupoid G and each locally constant 2-cocycle σ on G taking values in the units , we study the algebra consisting of locally constant compactly supported R-valued functions on G, with convolution and involution “twisted” by σ. We also introduce a “discretised” analogue of a twist Σ over a Hausdorff étale groupoid G, and we show that there is a one-to-one correspondence between locally constant 2-cocycles on G and discrete twists over G admitting a continuous global section. Given a discrete twist Σ arising from a locally constant 2-cocycle σ on an ample Hausdorff groupoid G, we construct an associated twisted Steinberg algebra , and we show that it coincides with . Given any discrete field , we prove a graded uniqueness theorem for , and under the additional hypothesis that G is effective, we prove a Cuntz–Krieger uniqueness theorem and show that simplicity of is equivalent to minimality of G. 相似文献
9.
Quantum Yang-Baxter module algebras 总被引:10,自引:0,他引:10
LetH be a quantum group over a commutative ringR. We introduce the concept of quantum Yang-BaxterH-module algebra, generalizing the notion ofH-dimodule algebra in the case whereH is commutative, cocommutative and faithfully projective. After discussing some examples, we introduceH-Azumaya algebras. The set of quivalence classes ofH-Azumaya algebras can be made into a group, called the Brauer group of the quantum groupH. This group is a generalization of the Brauer-Long group.This author wishes to thank the Department of Mathematics, UIA, for its hospitality and financial support during the time when most of this paper was written. 相似文献
10.
Xiao-yuan Chen 《高校应用数学学报(英文版)》2008,23(3):366-370
Results of the research for smash product algebras over dimodule algebras are generalized to the more general twisted dimodule algebras. 相似文献
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12.
S. Caenepeel F. Van Oystaeyen Y. H. Zhang 《Transactions of the American Mathematical Society》1997,349(9):3737-3771
Let be a Hopf algebra with bijective antipode. In a previous paper, we introduced -Azumaya Yetter-Drinfel'd module algebras, and the Brauer group classifying them. We continue our study of , and we generalize some properties that were previously known for the Brauer-Long group. We also investigate separability properties for -Azumaya algebras, and this leads to the notion of strongly separable -Azumaya algebra, and to a new subgroup of the Brauer group .
13.
We construct the Grothendieck rings of a class of 2n2dimensional semisimple Hopf Algebras H2n2,which can be viewed as a generalization of the 8 dimensional Kac-Paljutkin Hopf algebra H8.All irreducible H2n2-modules are classified.Furthermore,we describe the Grothendieck rings r(H2n2)by generators and relations explicitly. 相似文献
14.
We present a general construction producing a unitary corepresentation of a multiplier Hopf algebra in itself and study RR-corepresentations of twisted tensor coproduct multiplier Hopf algebra. Then we investigate some properties of functors, integrals and morphisms related to the categories of the crossed modules and covariant modules over multiplier Hopf algebras. By doing so, we can apply our theory to the case of group-cograded multiplier Hopf algebras, in particular, the case of Hopf group-coalgebras. 相似文献
15.
George E. Andrews Li Guo William Keigher Ken Ono 《Transactions of the American Mathematical Society》2003,355(11):4639-4656
By applying a recent construction of free Baxter algebras, we obtain a new class of Hopf algebras that generalizes the classical divided power Hopf algebra. We also study conditions under which these Hopf algebras are isomorphic.
16.
Bangming Deng 《中国科学A辑(英文版)》2000,43(11):1164-1173
This paper gives a complete classification of ℱ( Δ)-finite twisted double incidence algebras of posets in the case where the
Hasse quivers of posets are of type An. 相似文献
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18.
Nicolas Andruskiewitsch Sonia natale Nicolas Andruskiewitsch sonia natale 《代数通讯》2013,41(10):3239-3254
In this paper we discuss the structure of some product G =AB of nilpotent subgroups A and B. In particular we prove that if G is a minimax soluble group or a finitely generated linear group and if it does not have non-trivial periodic normal subgroups, then G is metanilpotent. 相似文献
19.
In this paper, we define the notion of self-dual graded weak Hopf algebra and self-dual semilattice graded weak Hopf algebra. We give characterization of finite-dimensional such algebras when they are in structually simple forms in the sense of E. L. Green and E. N. Morcos. We also give the definition of self-dual weak Hopf quiver and apply these types of quivers to classify the finite- dimensional self-dual semilattice graded weak Hopf algebras. Finally, we prove partially the conjecture given by N. Andruskiewitsch and H.-J. Schneider in the case of finite-dimensional pointed semilattice graded weak Hopf algebra H when grH is self-dual. 相似文献
20.
扭曲的自对偶Hopf代数 总被引:2,自引:1,他引:1
从两种重要的结构crossed积代数和扭曲Smash余积余代数出发,构造了一类新的Hopf代数R(?)K#_σH,并讨论它成为自对偶Hopf代数的条件. 相似文献