On Categories associated to a Quasi-Hopf algebra

2014/02/06 by Štefan Sakáloš, Sakáloš, Štefan
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math.QA

paper · pdf · doi:10.48550/arxiv.1402.1393

Bibliography corrected in arXiv v2

openalex publication_date 2014/02/06 · arxiv created 2014/02/13 · arxiv updated 2014/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A quasi-Hopf algebra H can be seen as a commutative algebra A in the centre \mathcal Z(H-Mod) of H-Mod. We show that the category of A-modules in \mathcal Z(H-Mod) is equivalent (as a monoidal category) to H-Mod. This can be regarded as a generalization of the structure theorem of Hopf bimodules of a Hopf algebra to the quasi-Hopf setting.

Citations

• Integral Theory for Quasi-Hopf Algebras

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• Two characterizations of finite quasi-Hopf algebras
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