Generalized (anti) Yetter-Drinfeld modules as components of a braided T-category期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Authors:	Florin Panaite Mihai D Staic

Institution:	(1) Present address: Institute of Mathematics of the Romanian Academy, PO-Box 1-764, RO-014700 Bucharest, Romania;(2) Department of Mathematics, SUNY at Buffalo, Amherst, NY 14260-2900, USA

Abstract:	If H is a Hopf algebra with bijective antipode and α, β ∈ Aut _Hopf(H), we introduce a category $_H \mathcal{Y}\mathcal{D}^H (\alpha ,\beta )$ , generalizing both Yetter-Drinfeld modules and anti-Yetter-Drinfeld modules. We construct a braided T-category $\mathcal{Y}\mathcal{D}(H)$ having all the categories $_H \mathcal{Y}\mathcal{D}^H (\alpha ,\beta )$ 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 $_H \mathcal{Y}\mathcal{D}^H (\alpha ,\beta )$ is isomorphic to the category of usual Yetter-Drinfeld modules $_H \mathcal{Y}\mathcal{D}^H$ . Research partially supported by the programme CERES of the Romanian Ministry of Education and Research, contract no. 4-147/2004.

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