Some isomorphisms for the Brauer groups of a Hopf algebra

2000/05/17 by Giovanna Carnovale, Carnovale, Giovanna
Mathematics · #13A20 18D10 16H05 (Secondary) #16W30 (Primary) #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #math.AC #math.RT #msc:13A20 #msc:16H05 #msc:16W30 #msc:18D10

paper · pdf · doi:10.48550/arxiv.math/0005177

23 pages, minor changes, one reference added

openalex publication_date 2000/05/17 · arxiv created 2000/05/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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,H₄,r_t) for every dual quasitriangular structure r_t on Sweedler's Hopf algebra H₄ 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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