On Corepresentations of Multiplier Hopf Algebras  

作　　者：Shuan-hong WANG Hai-xing ZHU 

机构地区：[1]Department of Mathematics, Southeast University, Nanjing 210096, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2010年第6期1087-1114,共28页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China (Grant No. 10871042); the Research Fund for the Doctoral Program of Higher Education (Grant No. 20060286006); Natural Science Foundation of Jiangsu Province (Grant No. BK2009258);the Key Project of Chinese Ministry of Education of China (Grant No.108154)

摘　　要：We present a general construction producing a unitary corepresentation of a multiplier Hopf algebra in itself and study RR-corepresentations of twisted tensor coproduct multiplier Hopf algebra. Then we investigate some properties of functors, integrals and morphisms related to the categories of the crossed modules and covariant modules over multiplier Hopf algebras. By doing so, we can apply our theory to the case of group-cograded multiplier Hopf algebras, in particular, the case of Hopf group-coalgebras.We present a general construction producing a unitary corepresentation of a multiplier Hopf algebra in itself and study RR-corepresentations of twisted tensor coproduct multiplier Hopf algebra. Then we investigate some properties of functors, integrals and morphisms related to the categories of the crossed modules and covariant modules over multiplier Hopf algebras. By doing so, we can apply our theory to the case of group-cograded multiplier Hopf algebras, in particular, the case of Hopf group-coalgebras.

关 键 词：（group-cograded） multiplier Hopf algebra copresentation crossed module covariant module Hopf group-coalgebra twisted tensor coproduct 

分 类 号：O153.3[理学—数学] O121.4[理学—基础数学]