Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

When weak Hopf algebras are Frobenius


Authors: Miodrag Cristian Iovanov and Lars Kadison
Journal: Proc. Amer. Math. Soc. 138 (2010), 837-845
MSC (2000): Primary 18D10; Secondary 16W30, 16S50, 16D90, 16L30
Published electronically: October 22, 2009
MathSciNet review: 2566549
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We investigate when a weak Hopf algebra $ H$ is Frobenius. We show this is not always true, but it is true if the semisimple base algebra $ A$ has all its matrix blocks of the same dimension. However, if $ A$ is a semisimple algebra not having this property, there is a weak Hopf algebra $ H$ with base $ A$ which is not Frobenius (and consequently, it is not Frobenius ``over'' $ A$ either). Moreover, we give a categorical counterpart of the result that a Hopf algebra is a Frobenius algebra for a noncoassociative generalization of a weak Hopf algebra.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 18D10, 16W30, 16S50, 16D90, 16L30

Retrieve articles in all journals with MSC (2000): 18D10, 16W30, 16S50, 16D90, 16L30


Additional Information

Miodrag Cristian Iovanov
Affiliation: Faculty of Mathematics, University of Bucharest, Str. Academiei 14, RO-70109, Bucharest, Romania – and – State University of New York, Buffalo, 244 Mathematics Building, Buffalo, New York 14260-2900
Email: yovanov@gmail.com, e-mail@yovanov.net

Lars Kadison
Affiliation: Department of Mathematics, University of Pennsylvania, David Rittenhouse Laboratory, 209 S. 33rd Street, Philadelphia, Pennsylvania 19104
Address at time of publication: Department of Mathematics, University of California at San Diego, 9500 Gilman Drive, #0112, La Jolla, California 92093
Email: lkadison@math.upenn.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10121-1
PII: S 0002-9939(09)10121-1
Keywords: Weak Hopf algebra, quasi-Hopf algebra, Frobenius algebra, quasi-Frobenius algebra, tensor category, Tannakian reconstruction
Received by editor(s): November 20, 2008
Received by editor(s) in revised form: July 15, 2009
Published electronically: October 22, 2009
Additional Notes: The first author was partially supported by contract no. 24/28.09.07 with UEFISCU “Groups, quantum groups, corings and representation theory” of CNCIS, PN II (ID_1002).
Communicated by: Martin Lorenz
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.