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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A structure theorem for quasi-Hopf comodule algebras


Authors: Florin Panaite and Freddy Van Oystaeyen
Journal: Proc. Amer. Math. Soc. 135 (2007), 1669-1677
MSC (2000): Primary 16, 17
Published electronically: February 12, 2007
MathSciNet review: 2286074
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Abstract: If $ H$ is a quasi-Hopf algebra and $ B$ is a right $ H$-comodule algebra such that there exists $ v:H\rightarrow B$ a morphism of right $ H$-comodule algebras, we prove that there exists a left $ H$-module algebra $ A$ such that $ B\simeq A\char93 H$. The main difference when comparing to the Hopf case is that, from the multiplication of $ B$, which is associative, we have to obtain the multiplication of $ A$, which in general is not; for this we use a canonical projection $ E$ arising from the fact that $ B$ becomes a quasi-Hopf $ H$-bimodule.


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Additional Information

Florin Panaite
Affiliation: Institute of Mathematics of the Romanian Academy, PO-Box 1-764, RO-014700 Bucharest, Romania
Email: Florin.Panaite@imar.ro

Freddy Van Oystaeyen
Affiliation: Department of Mathematics and Computer Science, University of Antwerp, Middelheimlaan 1, B-2020 Antwerp, Belgium
Email: Francine.Schoeters@ua.ac.be

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08712-6
PII: S 0002-9939(07)08712-6
Received by editor(s): July 19, 2005
Received by editor(s) in revised form: March 7, 2006
Published electronically: February 12, 2007
Additional Notes: This research was partially supported by the EC programme LIEGRITS, RTN 2003, 505078, and by the bilateral project “New techniques in Hopf algebras and graded ring theory” of the Flemish and Romanian Ministries of Research. The first author was also partially supported by the programme CERES of the Romanian Ministry of Education and Research, contract no. 4-147/2004.
Communicated by: Martin Lorenz
Article copyright: © Copyright 2007 American Mathematical Society