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