Algebraic deformation quantization of Leibniz algebras

• Main Authors: Alexandre, Charles, Bordemann, Martin, Riviere, Salim, Wagemann, Friedrich
• Format: Journal Article
• Language: English
• Published: 08-10-2018
• Subjects: Mathematics - Algebraic Topology; Mathematics - Quantum Algebra
• DOI: 10.48550/arxiv.1810.04050

Communications in Algebra, Taylor & Francis, 2018 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.