Representation theory of the Drinfel'd doubles of a family of Hopf algebras

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We investigate the Drinfel'd doubles $D(Λ_{n,d})$ 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 Drinfel'd doubles, from which we deduce properties of their representations, including the Auslander-Reiten quivers of the $D(Λ_{n,d})$. 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.
32 pages, uses xy diagrams, submitted

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Representation Theory, Quantum Algebra, 17B37, 06B15, 81R50, 16W30, 16W35, 16G20, 16G70, 18D10

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http://salesiana.dossiersoluciones.com/handle/123456789/72703

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0410017
 http://arxiv.org/abs/math/0410017

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arXiv