When weak Hopf algebras are Frobenius

Iovanov, Miodrag; Kadison, Lars

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

When weak Hopf algebras are Frobenius
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by Miodrag Cristian Iovanov and Lars Kadison PDF

Proc. Amer. Math. Soc. 138 (2010), 837-845 Request permission

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.

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