Anti-Yetter–Drinfeld Modules for Quasi-Hopf Algebras

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 followup 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.