Open Access
2016 Structure Theory of Rack-Bialgebras
C Alexandre, M Bordemann, S Rivière, F Wagemann
J. Gen. Lie Theory Appl. 10(1): 1-20 (2016). DOI: 10.4172/1736-4337.1000244


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 wellknown 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 dialgebras.


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C Alexandre. M Bordemann. S Rivière. F Wagemann. "Structure Theory of Rack-Bialgebras." J. Gen. Lie Theory Appl. 10 (1) 1 - 20, 2016.


Published: 2016
First available in Project Euclid: 3 February 2017

zbMATH: 06685548
MathSciNet: MR3652756
Digital Object Identifier: 10.4172/1736-4337.1000244

Keywords: Canonical rack bialgebras , coalgebras , Cocommutative Hopf dialgebras , Drinfeld center , Manifolds

Rights: Copyright © 2016 Ashdin Publishing (2009-2013) / OMICS International (2014-2016)

Vol.10 • No. 1 • 2016
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