紧矩阵量子群G的余表示与其对偶量子群的关系  

The Relation Between Corepesentation of a Compact Matrix Quantum Group G and Its Dual Quantum Group A

作　　者：张小霞[1] 张伦传[2] 

机构地区：[1]曲阜师范大学数学系 [2]人民大学信息学院,北京100090

出　　处：《数学学报（中文版）》2002年第6期1149-1156,共8页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目

摘　　要：设 G=（A,△）为紧矩阵量子群,G为A的所有有限维光滑的、不可约余表示等价类的集合.本文通过（A,△）的一个余表示Vo构造了两个相互配对的集合,利用Hilbert C＊-模的理论证明它们分别为A和Baaj与Skandalis构造的量子群A,并且证明了对任意的α∈G,在A中都对应一个有限维投影算子Pα,满足 dim（α）=dim（pα）.Abstract Let G = (A, A) be a compact matrix quantum group, G the equivalent set of all finite, smooth, irreducible corepresentations of A. In this paper, via a special corepresentation V0 of A, we construct a pair of sets, and using the theory of Hilbert C*-module, we prove that they are exactly A and A respectively, where A corresponds to Baaj and Skandalis-construction. We also prove that for any a ? G there exists a projective operator pa in A such that dim(α) = dim(pα).

关 键 词：对偶量子群 紧矩阵量子群 余表示 HILBERT C^＊-模 

分 类 号：O152.5[理学—数学] O177.1[理学—基础数学]