When weak Hopf algebras are Frobenius
Quantum Algebra
2009-07-15 v3 Rings and Algebras
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). 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.
Keywords
Cite
@article{arxiv.0810.4777,
title = {When weak Hopf algebras are Frobenius},
author = {Miodrag C. Iovanov and Lars Kadison},
journal= {arXiv preprint arXiv:0810.4777},
year = {2009}
}
Comments
8 pp., to appear in Proc. A.M.S