Cocycle twisting of E(n)-module algebras and applications to the Brauer group

2004/03/25 by Giovanna Carnovale, G. Carnovale, Carnovale, G. +3 · 2 citations
Mathematics · Physics and Astronomy · #16H05 #16K50 #16W30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.RA #math.RT #msc:16H05 #msc:16K50 #msc:16W30

paper · pdf · doi:10.48550/arxiv.math/0403444

Accidentally an old version of the paper was posted. Main corrections are in Section 2 and in Section 4.2

openalex publication_date 2004/03/25 · arxiv created 2004/04/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify the orbits of coquasi-triangular structures for the Hopf algebra E(n) under the action of lazy cocycles and the Hopf automorphism group. This is applied to detect subgroups of the Brauer group BQ(k,E(n)) of E(n) that are isomorphic. For a triangular structure R on E(n) we prove that the subgroup BM(k,E(n),R) of BQ(k,E(n)) arising from R is isomorphic to a direct product of BW(k), the Brauer-Wall group of the ground field k, and Sym_n(k), the group of n × n symmetric matrices under addition. For a general quasi-triangular structure R' on E(n) we construct a split short exact sequence having BM(k,E(n), R') as a middle term and as a left term a central extension of the group of symmetric matrices of order r

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