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arXiv · 1810.04050

Algebraic deformation quantization of Leibniz algebras

Charles Alexandre·Martin Bordemann·Salim Riviere·Friedrich Wagemann
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Abstract

In this paper we focus on a certain self-distributive multiplication on coalgebras, which leads to so-called rack bialgebra. We construct canon-ical rack bialgebras (some kind of enveloping algebras) for any Leibniz algebra. Our motivation is deformation quantization of Leibniz algebras in the sense of [6]. Namely, the canonical rack bialgebras we have constructed for any Leibniz algebra lead to a simple explicit formula of the rack-star-product on the dual of a Leibniz algebra recently constructed by Dherin and Wagemann in [6]. We clarify this framework setting up a general deformation theory for rack bialgebras and show that the rack-star-product turns out to be a deformation of the trivial rack bialgebra product.

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Charles Alexandre, Martin Bordemann, Salim Riviere, Friedrich Wagemann. 2018-10-08. Algebraic deformation quantization of Leibniz algebras. https://arxiv.org/abs/1810.04050

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