When weak Hopf algebras are Frobenius

Miodrag Cristian Iovanov; Lars Kadison

doi:10.1090/S0002-9939-09-10121-1

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When weak Hopf algebras are Frobenius

Miodrag Cristian Iovanov and Lars Kadison

Proceedings of the American Mathematical Society, Vol.138(3), pp.837-845

2010

DOI: 10.1090/S0002-9939-09-10121-1

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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.

Details

Title: Subtitle: When weak Hopf algebras are Frobenius
Creators: Miodrag Cristian Iovanov - University of Iowa, Mathematics
Lars Kadison
Resource Type: Journal article
Publication Details: Proceedings of the American Mathematical Society, Vol.138(3), pp.837-845
DOI: 10.1090/S0002-9939-09-10121-1
ISSN: 0002-9939
eISSN: 1088-6826
Publisher: American Mathematical Society
Language: English
Date published: 2010
Academic Unit: Mathematics
Record Identifier: 9983985876902771

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