三角Hopf代数表示范畴上的Lie余代数

本文在三角Ｈｏｐｆ代数表示范畴上系统地研究了Ｌｉｅ余代数,在此范畴上 的Ｌｉｅ余代数与Ｈｏｐｆ代数之间建立了重要的联系．主要给出了Ｌｉｅ余代数的余包络 余代数的结构．所得结果自然是关于Ｌｉｅ代数的对偶结果,推广了 Ｓｗｅｅｄｌｅｒ Ｍ． Ｅ．, Ｇｕｒｅｖｉｃｈ Ｄ．Ｉ．, Ｍｉｃｈａｅｌｉｓ Ｗ．和 Ｍａｉｉｄ Ｓ．等人的结果．     

Constructing New Quasitriangular Turaev Group Coalgebras

In this article, we construct a lot of new examples of Hopf group coalgebras by considering Majid's bicrossproduct Hopf algebra in Turaev category. Furthermore, we find the sufficient and necessary conditions for such Majid's bicrossproduct Hopf algebra to admit quasitriangular structures in the sense of Turaev group coalgebras.     

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．     

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.     

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.     

A Trace-Like Invariant for Representations of Hopf Algebras

We introduce an invariant for the irreducible representations of finite dimensional Hopf algebras, defined as the trace of a map induced by the antipode on the endomorphisms of each corresponding simple module. We also compute the value of this invariant for the representations of two families of non-semisimple Hopf algebras.     

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.     

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.     

模余代数的结构定理(英文)

This paper,mainly gives the structure theorem for module coalgebras by a kind of new method,and deletes the condition that the antipode S of the Hopf algebra H is bijective.     

On the Decomposition of Hopf Module Coalgebra

In1969,Sweedler[1]giventhedecompositiontheoreyofcoalgebraswhicharecocommu-tative.In1975,Kaplansky[2]showedthatanycoalgebracanbeuniquelydecomposedintoadirectsumofitsindecomposablesubcoalgebras.From1978to1992,Shudo[3]andXu[4]consructuredtheindecomposabledirectsumcomponentsofacoalggebra,viadefineequivalenceralationforthesetofsimplesubcoalgebras.Asweknow,themodolecoalgebraisthennaturalgeneralizationofcoalgebra.AndittakesplayanimportentroleintheDrinfelddouble.Inthispaper,wediscussthedecompositio…     

Prime-Dimensional Hopf Algebras

Ｐｒｉｍｅ－ＤｉｍｅｎｓｉｏｎａｌＨｏｐｆＡｌｇｅｂｒａｓＣａｉＣｈｕａｎｒｅｎ（蔡传仁）ａｎｄＣｈｅｎＨｕｉｘｉａｎｇ（陈惠香）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＹａｎｇｚｈｏｕＴｅａｃｈｅｒ＇ｓＣｏｌｌｅｇｅ，Ｊｉａｎｇｓｕ２２５...     

交叉余积上的Hopf代数结构

本文给出了Ｓｍａｓｈ积代数结构和交叉余积余代数结构构成双代数的一个充分必要条件．另外,还给出了这一新的双代数成为Ｈｏｐｆ代数的一个充分条件．     

相关Hopf模的对偶

本文的目的就是给出相关Hopf模的对偶性质.在第一部分,证明了相关Hopf模的对偶模仍是相关Hopf模.特别地,Hopf模的对偶仍是Hopf模.在第二、第三两部分,分别给出相关Hopf模的对偶相关Hopf模的基本结构定理及Maschke定理.     

Constructing the Co cyclic Structures for Crossed Copro duct Coalgebras

In this paper, we construct a cocylindrical object associated to two coal-gebras and a cotwisted map. It is shown that there exists an isomorphism between the cocyclic object of the crossed coproduct c...     

用quiver构造拟三角Hopf代数

利用quiver方法确定了一个广义Taft代数具有拟三角Hopf结构当且仅当它是Sweedler 4维Hopf代数．用不同于文[15]的方法,对任意的正整数n,构造出一类拟三角Hopf代数H(n)．     

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.     

Dual Coalgebras of Jordan Bialgebras and Superalgebras

W. Michaelis showed for Lie bialgebras that the dual coalgebra of a Lie algebra is a Lie bialgebra. In the present article we study an analogous question in the case of Jordan bialgebras. We prove that a simple infinite-dimensional Jordan superalgebra of vector type possesses a nonzero dual coalgebra. Thereby, we demonstrate that the hypothesis formulated by W. Michaelis for Lie coalgebras fails in the case of Jordan supercoalgebras.