无限维余Frobenius Hopf代数对角交叉积的表示范畴  

THE REPRESENTATION CATEGORIES OF DIAGONAL CROSSED PRODUCTS OF INFINITE-DIMENSIONAL COFROBENIUS HOPF ALGEBRAS

作　　者：杨涛[1] 刘慧丽 YANG Tao;LIU Hui-li(College of Science,Nanjing Agricultural University,Nanjing 210095,China)

机构地区：[1]南京农业大学理学院,江苏南京210095

出　　处：《数学杂志》2021年第6期495-502,共8页Journal of Mathematics

基　　金：Supported by China Postdoctoral Science Foundation(2019M651764);National Natural Science Foundation of China(11601231)。

摘　　要：本文研究了无限维余Frobenius Hopf代数对角交叉积表示范畴刻画的问题.利用乘子Hopf代数以及同调代数理论中的方法,获得了无限维余Frobenius Hopf代数对角交叉积的表示范畴与广义Yetter-Drinfeld范畴同构的结果,推广了Panaite等人在有限维Hopf代数中的结果.The categorical interpretations on representations of diagonal crossed products of infinite-dimensional coFrobenius Hopf algebras are studied in this paper.By the tools of multiplier Hopf algebra and homological algebra theories,we get that the unital representation category of a diagonal crossed product of an infinite-dimensional coFrobenius Hopf algebra is isomorphic to its generalized Yetter-Drinfeld category,which generalizes the results of Panaite et al.in finitedimensional case.

关 键 词：余Frobenius Hopf代数 对角交叉积 Yetter-Drinfel’d模 

分 类 号：O153.3[理学—数学]