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 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.
Keywords
Cite
@article{arxiv.1804.02031,
title = {Anti-Yetter-Drinfeld Modules for Quasi-Hopf Algebras},
author = {Ivan Kobyzev and Ilya Shapiro},
journal= {arXiv preprint arXiv:1804.02031},
year = {2018}
}
Comments
This is a follow-up paper to arXiv:1803.09194. Section 3 (definition and properties of quasi-Hopf algebra) mostly overlaps