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

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.