Deformation quantization of Leibniz algebras | Vidéo | Carmin.tv

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Deformation quantization of Leibniz algebras

By Friedrich Wagemann

Appears in collections : Algebra, deformations and quantum groups / Algèbre, déformations et groupes quantiques, Exposés de recherche

Let $\mathfrak{h}$ be a finite dimensional real Leibniz algebra. Exactly as the linear dual space of a Lie algebra is a Poisson manifold with respect to the Kostant-Kirillov-Souriau (KKS) bracket, $\mathfrak{h}^²$ can be viewed as a generalized Poisson manifold. The corresponding bracket is roughly speaking the evaluation of the KKS bracket at $0$ in one variable. This (perhaps strange looking) bracket comes up naturally when quantizing $\mathfrak{h}^²$ in an analoguous way as one quantizes the dual of a Lie algebra. Namely, the product $X \vartriangleleft Y = exp(ad_X)(Y)$ can be lifted to cotangent level and gives than a symplectic micromorphism which can be quantized by Fourier integral operators. This is joint work with Benoit Dherin (2013). More recently, we developed with Charles Alexandre, Martin Bordemann and Salim Rivire a purely algebraic framework which gives the same star-product.

Information about the video

Date of recording 04/12/2014
Date of publication 11/12/2014
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.18647403
Cite this video Wagemann, Friedrich (04/12/2014). Deformation quantization of Leibniz algebras. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.18647403
URL https://dx.doi.org/10.24350/CIRM.V.18647403

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Bibliography

Dherin, B., & Wagemann, F. (2014). Deformation quantization of Leibniz algebras. Preprint, arXiv:1310.6854v2 [math.SG] - http://arxiv.org/abs/1310.6854

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