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 language | English |
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Publisher | ArXiv |
Number of pages | 55 |
Publication status | Published - 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.)