Poisson-Lie structures as shifted Poisson structures

2017/06/08 by Safronov, Pavel
#Algebraic Geometry (math.AG) #FOS: Mathematics #Quantum Algebra (math.QA) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1706.02623

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.

Related

• Shifted Poisson structures on higher Chevalley-Eilenberg algebras
• Group-like objects in Poisson geometry and algebra
• Poisson Lie groups and Hamiltonian theory of the Yang-Baxter maps
• Deformation Quantization of Certain Non-linear Poisson Structures
• Comparison of Poisson structures and Poisson-Lie dynamical r-matrices