Doi-Hopf modules and Yetter-Drinfeld modules for quasi-Hopf algebras

Bulacu, D.; Caenepeel, S.; Torrecillas, B.

Doi-Hopf modules and Yetter-Drinfeld modules for quasi-Hopf algebras

Authors

Bulacu, D.

Caenepeel, S.

Torrecillas, B.

Description

For a quasi-Hopf algebra $H$, a left $H$-comodule algebra $\mf{B}$ and a right $H$-module coalgebra $C$ we will characterize the category of Doi-Hopf modules ${}^C{\cal M}(H)_{\mf{B}}$ in terms of modules. We will also show that for an $H$-bicomodule algebra $\mb{A}$ and an $H$-bimodule coalgebra $C$ the category of generalized Yetter-Drinfeld modules ${}_{\mb{A}}{\cal YD}(H)^C$ is isomorphic to a certain category of Doi-Hopf modules. Using this isomorphism we will transport the properties from the category of Doi-Hopf modules to the category of generalized Yetter-Drinfeld modules.
31 pages