On the structure and representations of non-balanced quantum doubles  

作　　者：CHEN Li-li LI Fang 

机构地区：[1]College of Mathematics and Physics,Qingdao University of Science and Technology,Qingdao 266061,China [2]Department of Mathematics,Zhejiang University,Hangzhou 310027,China

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2012年第4期475-488,共14页高校应用数学学报（英文版）（B辑）

基　　金：Supported by Doctoral Foundation of Qingdao University of Science and Technology (20080022398);the National Natural Science Foundation of China (11271318, 11171296);the Specialized Research Fund for the Doctoral Program of Higher Education of China (20110101110010)

摘　　要：For a field k and two finite groups G and X, when G acts on X from the right by group automorphisms, there is a Hopf algebra structure on k-space （kX°P）＊ kG （see Theorem 2.1）, called a non-balanced quantum double and denoted by Dx（G）. In this paper, some Hopf algebra properties of Dx （G） are given, the representation types of Dx （G） viewed as a k-algebra are discussed, the algebra structure and module category over Dx（G） are studied. Since the Hopf algebra structure of non-balanced quantum double DX （G） generMizes the usual quantum double D（G） for a finite group G, all results about Dx（G） in this paper can also be used to describe D（G） as a special case and the universal R-matrix of Dx （G） provides more solutions of Yang-Baxter equation.For a field k and two finite groups G and X, when G acts on X from the right by group automorphisms, there is a Hopf algebra structure on k-space （kX°P）＊ kG （see Theorem 2.1）, called a non-balanced quantum double and denoted by Dx（G）. In this paper, some Hopf algebra properties of Dx （G） are given, the representation types of Dx （G） viewed as a k-algebra are discussed, the algebra structure and module category over Dx（G） are studied. Since the Hopf algebra structure of non-balanced quantum double DX （G） generMizes the usual quantum double D（G） for a finite group G, all results about Dx（G） in this paper can also be used to describe D（G） as a special case and the universal R-matrix of Dx （G） provides more solutions of Yang-Baxter equation.

关 键 词：non-balanced quantum double Hopf Mgebra representation type quasi-triangularity quiver. 

分 类 号：O159[理学—数学] TK124[理学—基础数学]