二面体群上Hopf路余代数的结构分类

从Hopf quiver出发,借助于右kZ_u(c)-模的直积范畴■ Mkz_(u(C))与kG-Hopf双模范畴kG/kG M kG/kG之间的同构,当G是二面体群D_3时,给出了Hopf路余代数kQ~c的同构分类及其子Hopf代数kG[kQ_1]结构.     

二面体群上Hopf路余代数的结构分类

从Hopf quiver出发,借助于右kZu(C)-模的直积范畴ПC∈K(G) MkZu(C)与kG-Hopf双模范畴kG kG M kG kG之间的同构,当G是二面体群D3时,给出了Hopf路余代数kQc的同构分类及其子Hopf代数kG[kQ1]结构.     

三角Hopf余模范畴上的张量余代数

在三角Ｈｏｐｆ代数余模范畴上研究张量余代数．主要给出三角Ｈｏｐｆ代数余模范畴上的张量余代数的结构．     

交换Hopf代数扭余作用下的余代数的上同调

该文证明了若交换Hopf代数在余代数C上的扭余作用的coassociator是卷积可逆的,那么该扭余作用也是可逆的.在这种情形下,给出了余代数C的正则上同调的定义,并且证得每个可逆的扭余作用可以提升到H的系数属于C的一个三次正则上同调类,且扭余作用的obstruction是平凡的当且仅当该扭余作用对应着一个cleft余扩张.     

弱群余代数的交叉积

该文引入弱群交叉积的概念,并给出弱群交叉积代数和通常的张量积余代数构成弱半Hopf群余代数的充要条件,接着证明了弱群交叉积上的对偶定理,推广了沈和王~([7-8])的主要结果.     

Induced and Coinduced Representations of Hopf Group Coalgebras

The induction theory for a Hopf group coalgebra is outlined. Given a Hopf group coalgebra H, the notions of a quotient Hopf group coalgebra and group coisotropic quantum subgroup of H are introduced. The properties of (co)induced representations are studied and the geometric interpretation and simplicity theory of such representations are given.      

Constructing Quasitriangular Multiplier Hopf Algebras By Twisted Tensor Coproducts

Let A and B be multiplier Hopf algebras, and let R ∈ M(B ? A) be an anti-copairing multiplier, i.e, the inverse of R is a skew-copairing multiplier in the sense of Delvaux [5 Delvaux , L. ( 2004 ). Twisted tensor coproduct of multiplier Hopf (*)-algebras . J. Algebra 274 : 751 – 771 . [Google Scholar]]. Then one can construct a twisted tensor coproduct multiplier Hopf algebra A ? _R  B. Using this, we establish the correspondence between the existence of quasitriangular structures in A ? _R  B and the existence of such structures in the factors A and B. We illustrate our theory with a profusion of examples which cannot be obtained by using classical Hopf algebras. Also, we study the class of minimal quasitriangular multiplier Hopf algebras and show that every minimal quasitriangular Hopf algebra is a quotient of a Drinfel’d double for some algebraic quantum group.     

弱Hopf代数上的扭积

在弱Hopf代数上,定义了交叉积概念,并且得到了它的两种特殊形式,冲积和扭积．特别地,给出了扭积为弱Hopf代数的一个充要条件,推广了Hopf代数的相应结论．     

弱Hopf代数上的扭积

在弱Hopf代数上,定义了交叉积概念,并且得到了它的两种特殊形式冲积和扭积.特别地,给出了扭积为弱Hopf代数的一个充要条件,推广了Hopf代数的相应结论.     

Morita Contexts and Partial Group Galois Extensions for Hopf Group Coalgebras

We first introduce the notion of partial group twisted smash product and construct a Morita context for partial coaction of co-Frobenius Hopf group coalgebra relating generalized partial group smash product and partial coinvariants. Furthermore, we study group-Galois extensions and reobtain some classical results in the partial case. Finally, we prove that any partial group Galois extension induces a unique partial group entwining map compatible with the partial right coaction.     

交换群上Hopf路余代数的结构分类

设G是群, kG是域k上的群代数. 对任意Hopf箭向Q=(G, r), 利用右kZ_u(C) -模的直积范畴∏_C∈K(G) MkZ_u(C)与kG-Hopf双模范畴^kG_kG M^kG_kG之间的同构, 可由^u(C)(kQ₁)¹上的右kZ_u(C) -模结构导出在箭向余模kQ₁上的kG-Hopf双模结构. 该文讨论在群G分别是2阶循环群与克莱茵四元群时的Hopf路余代数kQ^c的同构分类及其子Hopf代数kG[kQ₁]结构.     

Tensor product of Hopf bimodules over a group

We describe the monoidal structure of the category of Hopf bimodules of a finite group and we derive a surjective ring map from the Grothendieck ring of the category of Hopf bimodules to the center of the integral group ring. We consider analogous results for the multiplicative structure of the Hochschild cohomology.

     

Tensor products of ideal codes over Hopf algebras

We study indecomposable codes over a family of Hopf algebras introduced by Radford. We use properties of Hopf algebras to show that tensors of ideal codes are ideal codes, extending the corresponding result that was previously given in the case of Taft Hopf algebras and showing the differences with that case.     

一类Hopf路余代数

设F是域,G是3阶循环群,Q是群G的箭图.借助于模范畴的等价性,给出了Hopf路余代数FQc的所有结构分类,并给出了FQc的子Hopf代数FG[FQc1]的结构.     

路余代数上的Hopf ε-代数

在q不为单位根时，本文用无限简图A∞∞的double路余代数KA∞∞^—的商代数同时实现了量子代数Uq（sl2）以及量子超代数Uq（ops（2，1））．     

一类Hopf路余代数

设F是域,G是3阶循环群,Q是群G的箭图.借助于模范畴的等价性,给出了Hopf路余代数FQ~c的所有结构分类,并给出了FQ~c的子Hopf代数FG[FQ_1~c]的结构.     

New Braided Crossed Categories and Drinfel'd Quantum Double for Weak Hopf Group Coalgebras

A simple and nice structure theorem for orthogroups was given by Petrich in 1987. In this paper, we consider a generalized orthogroup, that is, a quasi-completely regular semigroup with a band of idempotents in which its set of regular elements, namely, RegS, forms an ideal of S. A method of construction of such semigroups is provided and as a result, the Petrich structure theorem of orthogroups becomes an immediate corollary of our theorem on generalized orthogroups. An example of such generalized orthogroup is also constructed. This example provides some useful information for the construction of various kinds of quasi-completely regular semigroups.     

二面体群上的Hopf Ore扩张

In this paper, the Hopf Ore extension and corresponding module extension of the group algebra over dihedral group are studied. It turns out that the 1-dimensional and 2- dimensional simple representations can both be extended to the simple representations over a class of Hopf Ore extension.     

Cyclic Homology of Hopf Comodule Algebras and Hopf Module Coalgebras

Abstract

In this paper we construct a cylindrical module A ? ? for an ?-comodule algebra A, where the antipode of the Hopf algebra ? is bijective. We show that the cyclic module associated to the diagonal of A ? ? is isomorphic with the cyclic module of the crossed product algebra A ? ?. This enables us to derive a spectral sequence for the cyclic homology of the crossed product algebra. We also construct a cocylindrical module for Hopf module coalgebras and establish a similar spectral sequence to compute the cyclic cohomology of crossed product coalgebras.     

扭曲的自对偶Hopf代数

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.