Sweedler's dual of Hopf algebras in HHYDQCM  

HHYDQCM范畴上Hopf代数的Sweedler对偶

作　　者：Zhang Tao Wang Shuanhong 张涛;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3期364-366,共3页东南大学学报（英文版）

基　　金：The National Natural Science Foundation of China(No.11371088,11571173,11871144)。

摘　　要：Firstly,the notion of the left-left Yetter-Drinfeld quasicomodule M=(M,·,ρ)over a Hopf coquasigroup H is given,which generalizes the left-left Yetter-Drinfeld module over Hopf algebras.Secondly,the braided monoidal category HHYDQCM is introduced and the specific structure maps are given.Thirdly,Sweedler's dual of infinite-dimensional Hopf algebras in HHYDQCM is discussed.It proves that if(B,mB,μB,ΔB,εB)is a Hopf algebra in HHYDQCM with antipode SB,then(B^0,(mB0)^op,εB^*,(ΔB0)^op,μB^*)is a Hopf algebra in HHYDQCM with antipode SB^*,which generalizes the corresponding results over Hopf algebras.首先,给出了Hopf余拟群H上的左-左Yetter-Drinfeld拟余模M=(M,·,ρ)的概念,其为Hopf代数上的左-左Yetter-Drinfeld模结构的推广.其次,介绍了辫子张量范畴HHYDQCM的定义并且给出其具体的结构映射.最后,讨论辫子张量范畴HHYDQCM上的无限维Hopf代数Sweedler的对偶问题.证明了如果(B,mB,μB,ΔB,εB)是HHYDQCM上有对极SB的Hopf代数,那么(B^0,(mB0)^op,εB^*,(ΔB0)^op,μB^*)是HHYDQCM上有对极SB^*的Hopf代数,从而推广了Hopf代数上的相应结果.

关 键 词：Hopf(co)quasigroup Yetter-Drinfeld quasi(co)module braided monoidal category DUALITY 

分 类 号：O15[理学—数学]