Poisson-Lie structures as shifted Poisson structures

Research output: Working paper

Abstract

Classical limits of quantum groups give rise to multiplicative Poisson structures such as Poisson-Lie and quasi-Poisson structures. We relate them to the notion of a shifted Poisson structure which gives a conceptual framework for understanding classical (dynamical) r-matrices, quasi-Poisson groupoids and so on. We also propose a notion of a symplectic realization of shifted Poisson structures and show that Manin pairs and Manin triples give examples of such.
Original languageEnglish
PublisherArXiv
Number of pages55
Publication statusPublished - 18 Jun 2018

Keywords / Materials (for Non-textual outputs)

  • 53D17 Poisson manifolds; Poisson groupoids and algebroids
  • 14A30 Fundamental constructions in algebraic geometry involving higher and derived categories (homotopical algebraic geometry, derived algebraic geometry, etc.)

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