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

DOI:
https://doi.org/10.1090/S0002-9939-07-08712-6

Published electronically:
February 12, 2007

MathSciNet review:
2286074

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Abstract | References | Similar Articles | Additional Information

Abstract: If is a quasi-Hopf algebra and is a right -comodule algebra such that there exists a morphism of right -comodule algebras, we prove that there exists a left -module algebra such that . The main difference when comparing to the Hopf case is that, from the multiplication of , which is associative, we have to obtain the multiplication of , which in general is not; for this we use a canonical projection arising from the fact that becomes a quasi-Hopf -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:
https://doi.org/10.1090/S0002-9939-07-08712-6

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