Generalized (anti) Yetter-Drinfeld modules as components of a braided T-category

2005/03/21 by Florin Panaite, Panaite, Florin, Mihai D. Staic +1 · 1 citation
Mathematics · #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA

paper · pdf · doi:10.48550/arxiv.math/0503413

12 pages, Latex, no figures

arxiv created 2005/03/21 · arxiv updated 2009/12/01

Abstract

If H is a Hopf algebra with bijective antipode and α, β∈ Aut_Hopf(H), we introduce a category_H\cal YD^H(α, β), generalizing both Yetter-Drinfeld and anti-Yetter-Drinfeld modules. We construct a braided T-category \cal YD(H) having all these categories as components, which if H is finite dimensional coincides with the representations of a certain quasitriangular T-coalgebra DT(H) that we construct. We also prove that if (α, β) admits a so-called pair in involution, then_H\cal YD^H(α, β) is isomorphic to the category of usual Yetter-Drinfeld modules_H\cal YD^H.

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