Representation theory of the Drinfeld doubles of a family of Hopf algebras

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Abstract

We investigate the Drinfeld doubles D(Λn,d) of a certain family of Hopf algebras. We determine their simple modules and their indecomposable projective modules, and we obtain a presentation by quiver and relations of these Drinfeld doubles, from which we deduce properties of their representations, including the Auslander-Reiten quivers of the D(Λn,d). We then determine decompositions of the tensor products of most of the representations described, and in particular give a complete description of the tensor product of two simple modules. This study also leads to explicit examples of Hopf bimodules over the original Hopf algebras. © 2005 Elsevier B.V. All rights reserved.

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Erdmann, K., Green, E. L., Snashall, N., & Taillefer, R. (2006). Representation theory of the Drinfeld doubles of a family of Hopf algebras. Journal of Pure and Applied Algebra, 204(2), 413–454. https://doi.org/10.1016/j.jpaa.2005.05.003

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