Turaev辫子群范畴和Doi-Hopf模

设G是一个群.利用Turaev辫子群范畴的性质,在Doi-Hopf数据(H,A,C)上构造一个Turaev辫子G-范畴,其中H,A,C是Hopf代数.进一步,当C为有限维时,在一簇Smash积代数{A#~HC~*(α)}_(α∈G)上构造一个拟三角Turaev G-余代数A#~HC~*,其表示范畴与_AM^C(H)是同构的.

余ribbon Turaev π-代数

讨论了Turaev π-代数余模范畴中的pivotal群交叉结构和ribbon群交叉结构,引入余pivotal Turaev π-代数和余ribbon Turaev π-代数的定义,并分别给出Turaev π-代数伴有余pivotal结构和余ribon结构的充要条件.

Turaev群代数的群扭曲张量双积

本文引入了群扭曲张量双积的概念,这推广了由Caenepeel等引入的扭曲张量双积(或广义积),得到了该群扭曲张量双积是Turaev群代数的充要条件.

Turaev群代数Doi-Hopf模

设G是群,H是Turaev群代数.首先引入了G-H-模余代数,G-H-余模代数及Doi-Hopf G-模等概念,其次给出了Turaev群代数H的Doi-Hopf G-模范畴之间的一些关系,最后得出了α-G-YetterDrinfel'd模范畴YD_α(H)和Doi-Hopf G-模范畴~H_αM_(G-H)(HcopH)同构的结论,即α-G-Yetter-Drinfel'd模是特殊的Doi-Hopf G-模.

Quasitriangular Turaev Group Coalgebras and Radford＇s Biproduct

In this paper, we construct a new example of Hopf group coalgebras by con- sidering Radford＇s biproduct Hopf algebra in the Turaev category. Furthermore, we find some sufficient and necessary conditions for such Radford＇s biproduct Hopf algebra to admit quasitriangulax structures in the sense of Turaev group coalgebras.

A Note on Generalized Long Modules

Let HLB be the category of generalized Long modules, that is, H-modules and B-comodules over Hopf algebras B and H. We describe a new Turaev braided group category over generalized Long module HLB （S（π）） where the opposite group S（π） of the semidirect product of the opposite group πopof a group π by π. As an application, we show that this is a Turaev braided group-category HLBfor a quasitriangular Turaev group-coalgebra H and a coquasitriangular Turaev group-algebra B.

基于交叉结构的广义Yang-Baxter方程解系的再构造

构造并研究了Turaev群余代数上的Drinfeld扭曲,讨论了其相关性质及在群交叉表示范畴上的应用,证明了交叉拟三角结构在Drinfeld扭曲下的同构不变性,由此构造了新的广义Yang-Baxter方程的解系。