The construction of braided T-category via Yetter-Drinfeld-Long bimodules

2019/12/23 by Lu, Daowei, Ning, Yan, Wang, Dingguo
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1912.10654

Abstract

Let H₁ and H₂ be Hopf algebras which are not necessarily finite dimensional and α,β∈ Aut_Hopf(H₁), γ,δ∈ Aut_Hopf(H₂). In this paper, we introduce a category _H1LR_H2(α, β, γ, δ), generalizing Yetter-Drinfeld-Long bimodules and construct a braided T-category LR(H₁,H₂) containing all the categories _H1LR_H2(α, β, γ, δ) as components. We also prove that if (α, β, γ, δ) admits a quadruple in involution, then _H1LR_H2(α, β, γ, δ) is isomorphic to the usual category _H1LR_H2 of Yetter-Drinfeld-Long bimodules.

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