Diagonal crossed product of multiplier Hopf algebras  

乘子Hopf代数上的对角交叉积

作　　者：Yan Dongdong Wang Shuanhong 晏冬冬;王栓宏(东南大学数学学院,南京211189)

机构地区：[1]School of Mathematics, Southeast University, Nanjing 211189, China

出　　处：《Journal of Southeast University(English Edition)》2020年第2期241-244,共4页东南大学学报（英文版）

基　　金：The National Natural Science Foundation of China(No.11371088,11571173,11871144);the Natural Science Foundation of Jiangsu Province(No.BK20171348)。

摘　　要：Let A and B be two regular multiplier Hopf algebras.First,the notion of diagonal crossed product B#A of multiplier Hopf algebras is constructed using the bimodule algebra,which is a generalization of the diagonal crossed product in the sense of Hopf algebras.The result that the product in B#A is non-degenerate is given.Next,the definition of the comultiplicationΔ#on B#A is introduced,which is composed of the multiplierΔB(b)on B⊗B and the multiplierΔA(a)on A⊗A,and the elementΔ#(b⊗a)is a two-side multiplier of B#A⊗B#A,for any b∈B and a∈A.Then,a sufficient condition for B#A to be a regular multiplier Hopf algebra is described.In particular,Delvaux's main theorem in the case of smash products is generalized.Finally,these integrals on a diagonal crossed product of multiplier Hopf algebras are considered.设A和B是2个正则乘子Hopf代数.首先,使用双模代数构造了乘子Hopf代数上对角交叉积B#A的定义,推广了Hopf代数上的对角交叉积.给出了B#A上的积是非退化的结论.介绍了对角交叉积B#A上的余乘Δ#的概念,对于任意的b∈B和a∈A,它由B⊗B上的乘子ΔB(b)和A⊗A上的乘子ΔA(a)构成,且元素Δ#(b⊗a)是B#A⊗B#A上的双边乘子.然后,描述了对角交叉积B#A成为一个正则乘子Hopf代数的充分条件.特别地,推广了Delvaux在冲积情况下的主要定理.最后,考虑了乘子Hopf代数上对角交叉积的积分.

关 键 词：multiplier Hopf algebra bimodule algebra diagonal crossed product 

分 类 号：O15[理学—数学]