Using equivalences of categories we provide general isomorphisms between the Brauer groups of different Hopf algebras. One of those is used to prove that the Brauer groups BC(k, H_4, r(1)) 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.
Some isomorphisms for the Brauer groups of a Hopf algebra
CARNOVALE, GIOVANNA
2001
Abstract
Using equivalences of categories we provide general isomorphisms between the Brauer groups of different Hopf algebras. One of those is used to prove that the Brauer groups BC(k, H_4, r(1)) 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.
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