Some isomorphisms for the Brauer groups of a Hopf algebra

Details Some isomorphisms for the Brauer groups of a Hopf algebra Some isomorphisms for the Brauer groups of a Hopf algebra

2000-05-17

arxiv.org/abs/math/0005177v2

Mathematics

Representation Theory

23 pages, minor changes, one reference added

Scientific paper

Using equivalences of categories we provide isomorphisms between the Brauer groups of different Hopf algebras. As an example, we show that when k is a field of characteristic different from 2 the Brauer groups BC(k,H_4,r_t) for every dual quasitriangular structure r_t on Sweedler's Hopf algebra H_4 are all isomorphic to the direct sum of (k,+) and the Brauer-Wall group of k. We provide an isomorphism between the Brauer group of a Hopf algebra H and the Brauer group of the dual Hopf algebra H^* generalizing a result of Tilborghs. Finally we relate the Brauer groups of H and of its opposite and co-opposite Hopf algebras.

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