SOME ISOMORPHISMS FOR THE BRAUER GROUPS OF A HOPF ALGEBRA

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_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.

ACKNOWLEDGMENTS

This work has been carried out at the Universitaire Instelling Antwerpen (UIA) where the author had a post-doc position financed by the EC network “Algebraic Lie Representations” contract ERB-FMRX-CT97-0100. The author wishes to thank the UIA for the warm hospitality and Professor Fred Van Oystaeyen, Dr. Juan Cuadra and Dr. Yinhuo Zhang for valuable comments and useful discussions.

The author also wishes to thank the referee for pointing out reference [15], which allowed an improvement of the proof of Proposition 4.2.