When weak Hopf algebras are Frobenius

Details When weak Hopf algebras are Frobenius When weak Hopf algebras are Frobenius

2008-10-27

arxiv.org/abs/0810.4777v3

Mathematics

Quantum Algebra

8 pp., to appear in Proc. A.M.S

Scientific paper

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.

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