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Hopf modules and the double of a quasi-Hopf algebra
Author(s):
Peter
Schauenburg
Journal:
Trans. Amer. Math. Soc.
354
(2002),
3349-3378.
MSC (2000):
Primary 16W30
Posted:
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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Additional Information:
Peter
Schauenburg
Affiliation:
Mathematisches Institut der Universität München, Theresienstr. 39, 80333 München, Germany
Email:
schauen@rz.mathematik.uni-muenchen.de
DOI:
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
Posted:
April 1, 2002
Copyright of article:
Copyright
2002,
American Mathematical Society
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