Anti-Yetter-Drinfeld Modules for Quasi-Hopf Algebras

Abstract

We apply categorical machinery to the problem of defining anti-Yetter-Drinfeld modules for quasi-Hopf algebras. While a definition of Yetter-Drinfeld modules in this setting, extracted from their categorical interpretation as the center of the monoidal category of modules, has been given, none was available for the anti-Yetter-Drinfeld modules that serve as coefficients for a Hopf cyclic type cohomology theory for quasi-Hopf algebras. This is a follow-up paper to the authors' previous effort that addressed the somewhat different case of anti-Yetter-Drinfeld contramodule coefficients in this and in the Hopf algebroid setting.