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
DOI:
https://doi.org/10.1090/S0002-9947-02-02980-X
Published electronically:
April 1, 2002
MathSciNet review:
1897403
Full-text PDF
Abstract | References | Similar Articles | Additional Information
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:
https://doi.org/10.1090/S0002-9947-02-02980-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
