On tensor factorizations of Hopf algebras

Abstract : We prove a variety of results on tensor product factorizations of finite dimensional Hopf algebras (more generally Hopf algebras satisfying chain conditions in suitable braided categories). The results are analogs of well-known results on direct product factorizations of finite groups (or groups with chain conditions) such as Fitting's lemma and the uniqueness of the Krull-Remak-Schmidt factorization. We analyze the notion of normal (and conormal) Hopf algebra endomorphisms, and the structure of endomorphisms and automorphisms of tensor products. The results are then applied to compute the automorphism group of the Drinfeld double of a finite group in the case where the group contains an abelian factor. (If it doesn't, the group can be calculated by results of the first author.)
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Algebra and Number Theory, 2016, 10, 1, pp.61-87. <10.2140/ant.2016.10.61 >
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https://hal-univ-bourgogne.archives-ouvertes.fr/hal-01410931
Contributeur : Imb - Université de Bourgogne <>
Soumis le : mardi 6 décembre 2016 - 18:38:05
Dernière modification le : mercredi 7 décembre 2016 - 09:16:25

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Marc Keilberg, Peter Schauenburg. On tensor factorizations of Hopf algebras. Algebra and Number Theory, 2016, 10, 1, pp.61-87. <10.2140/ant.2016.10.61 >. <hal-01410931>

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