Algebraic deformation quantization of Leibniz algebras
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 def...
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08-10-2018
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| Abstract | 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. |
|---|---|
| AbstractList | 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. |
| Author | Alexandre, Charles Wagemann, Friedrich Bordemann, Martin Riviere, Salim |
| Author_xml | – sequence: 1 givenname: Charles surname: Alexandre fullname: Alexandre, Charles organization: LMJL – sequence: 2 givenname: Martin surname: Bordemann fullname: Bordemann, Martin organization: LMJL – sequence: 3 givenname: Salim surname: Riviere fullname: Riviere, Salim organization: LMJL – sequence: 4 givenname: Friedrich surname: Wagemann fullname: Wagemann, Friedrich organization: LMJL |
| BackLink | https://doi.org/10.48550/arXiv.1810.04050$$DView paper in arXiv |
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| Snippet | Communications in Algebra, Taylor & Francis, 2018 In this paper we focus on a certain self-distributive multiplication on
coalgebras, which leads to so-called... |
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| SubjectTerms | Mathematics - Algebraic Topology Mathematics - Quantum Algebra |
| Title | Algebraic deformation quantization of Leibniz algebras |
| URI | https://arxiv.org/abs/1810.04050 |
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