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

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.