Hopf modules and the double of a quasi-Hopf algebra

Schauenburg, Peter

doi:10.1090/S0002-9947-02-02980-X

Hopf modules and the double of a quasi-Hopf algebra
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by Peter Schauenburg

Trans. Amer. Math. Soc. 354 (2002), 3349-3378

DOI: https://doi.org/10.1090/S0002-9947-02-02980-X

Published electronically: April 1, 2002

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Abstract:

We give a different proof for a structure theorem of Hausser and Nill on Hopf modules over quasi-Hopf algebras. We extend the structure theorem to a classification of two-sided two-cosided Hopf modules by Yetter-Drinfeld modules, which can be defined in two rather different manners for the quasi-Hopf case. The category equivalence between Hopf modules and Yetter-Drinfeld modules leads to a new construction of the Drinfeld double of a quasi-Hopf algebra, as proposed by Majid and constructed by Hausser and Nill.

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