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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Hopf modules and the double of a quasi-Hopf algebra


Author: Peter Schauenburg
Journal: Trans. Amer. Math. Soc. 354 (2002), 3349-3378
MSC (2000): Primary 16W30
Published electronically: April 1, 2002
MathSciNet review: 1897403
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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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Additional Information

Peter Schauenburg
Affiliation: Mathematisches Institut der Universität München, Theresienstr. 39, 80333 München, Germany
Email: schauen@rz.mathematik.uni-muenchen.de

DOI: http://dx.doi.org/10.1090/S0002-9947-02-02980-X
PII: S 0002-9947(02)02980-X
Keywords: Quasi-Hopf algebra, quantum double, Yetter-Drinfeld module, Hopf module
Received by editor(s): April 10, 2001
Received by editor(s) in revised form: November 13, 2001
Published electronically: April 1, 2002
Article copyright: © Copyright 2002 American Mathematical Society