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H 1 Deformation quantization of Leibniz algebras

Auteurs : Wagemann, Friedrich (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : 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, $\mathfrak{h}^*$ 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 $\mathfrak{h}^*$ 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.

    Codes MSC :
    22Exx - Lie groups [For the topology of Lie groups and homogeneous spaces, see 57Sxx, 57Txx; for analysis thereon, see 43A80, 43A85, 43A90]
    53D55 - Deformation quantization, star products
    81R60 - Noncommutative geometry
    17A32 - Leibniz algebras

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 11/12/14
      Date de captation : 04/12/14
      Collection : Research talks ; Algebra ; Topology
      Format : quicktime ; audio/x-aac
      Durée : 00:44:07
      Domaine : Algebra ; Topology
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2014-12-04_Wagemann.mp4

    Informations sur la rencontre

    Nom de la rencontre : Algebra, deformations and quantum groups / Algèbre, déformations et groupes quantiques
    Organisateurs de la rencontre : Kulish, Peter ; Makhlouf, Abdenacer ; Paal, Eugen ; Schlichenmaier, Martin ; Stolin, Alexander
    Dates : 01/12/14 - 05/12/14
    Année de la rencontre : 2014

    Citation Data

    DOI : 10.24350/CIRM.V.18647403
    Cite this video as: Wagemann, Friedrich (2014). Deformation quantization of Leibniz algebras. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18647403
    URI : http://dx.doi.org/10.24350/CIRM.V.18647403


    Bibliographie

    1. 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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