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

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

2004-07-29

arxiv.org/abs/math/0407510v1

Mathematics

Quantum Algebra

31 pages

Scientific paper

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.

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