On the classification of compact quantum groups U_θ(2)

作     者：ZHANG XiaoXia Department of Mathematics,Yantai University,Yantai 264005,China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2010年第53卷第5期

页      面：256-269页

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China (Grant No.10971011) 

主　　题：compact quantum group comultiplication irreducible representation 

摘      要：In this paper,we show that the corepresentation of compact group Uθ(2) on the vector space is determined by its infinitesimal generators B0,B2,A0,A1 and A2,where θ is an irrational *** also show that B0 and B2 commute with Aj,j = 0,1,2,so B0,A0,A1 and A2 are sl(2,C) loop *** we exhibit all irreducible representations of Uθ(2),which are different from those of group U(2),and use above results to give the classification of quantum groups Uθ(2),which is analogous to that of irrational algebra Aθ.At the same time,we also give all the forms of automorphisms on quantum group Uθ(2).