%0 Journal Article
%T When weak Hopf algebras are Frobenius
%A Miodrag C. Iovanov
%A Lars Kadison
%J Mathematics
%D 2008
%I arXiv
%X 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). We give, moreover, a categorical counterpart of the result that a Hopf algebra is a Frobenius algebra for a noncoassociative generalization of weak Hopf algebra.
%U http://arxiv.org/abs/0810.4777v3