Structure theory of Rack-Bialgebras

Abstract : In this paper we focus on a certain self-distributive multiplication on coalgebras, which leads to so-called rack bialgebra. Inspired by semi-group theory (adapting the Suschkewitsch theorem), we do some structure theory for rack bialgebras and cocommutative Hopf dialgebras. We also construct canonical rack bialgebras (some kind of enveloping algebras) for any Leibniz algebra and compare to the existing constructions. We are motivated by a differential geometric procedure which we call the Serre functor: To a pointed differentible manifold with multiplication is associated its distribution space supported in the chosen point. For Lie groups, it is well-known that this leads to the universal enveloping algebra of the Lie algebra. For Lie racks, we get rack-bialgebras, for Lie digroups, we obtain cocommutative Hopf di-algebras.
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Article dans une revue
Journal of Generalized Lie Theory and Applications, Natalia Iyudu (Edinburgh), Abdenacer Makhlouf (Université Haute Alsace, France), Noriaki Kamiya (University of Aizu, Japan), 2016, 10 (1)
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https://hal.archives-ouvertes.fr/hal-01891841
Contributeur : Friedrich Wagemann <>
Soumis le : mercredi 10 octobre 2018 - 09:30:50
Dernière modification le : mardi 16 octobre 2018 - 14:26:02

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  • HAL Id : hal-01891841, version 1

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Charles Alexandre, Martin Bordemann, Salim Riviere, Friedrich Wagemann. Structure theory of Rack-Bialgebras. Journal of Generalized Lie Theory and Applications, Natalia Iyudu (Edinburgh), Abdenacer Makhlouf (Université Haute Alsace, France), Noriaki Kamiya (University of Aizu, Japan), 2016, 10 (1). 〈hal-01891841〉

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