Cocycle Deformations and Brauer Group Isomorphisms

2005/04/30 by Hui-Xiang Chen, Huixiang Chen, Chen, Huixiang +2
Mathematics · Physics and Astronomy · #16A16 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT #msc:16A16

paper · pdf · doi:10.48550/arxiv.math/0505003

33 pages, no figures

arxiv created 2005/04/30 · openalex publication_date 2005/04/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let H be a Hopf algebra over a commutative ring k with unity and σ:H⊗ H\longrightarrow k be a cocycle on H. In this paper, we show that the Yetter-Drinfeld module category of the cocycle deformation Hopf algebra H^σ is equivalent to the Yetter-Drinfeld module category of H. As a result of the equivalence, the "quantum Brauer" group BQ(k,H) is isomorphic to BQ(k,H^σ). Moreover, the group \Gal(\HR) constructed in \citeZ is studied under a cocycle deformation.

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