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arXiv · 1706.02623

Poisson-Lie structures as shifted Poisson structures

Pavel Safronov
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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.

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BibTeXRIS

Pavel Safronov. 2017-06-08. Poisson-Lie structures as shifted Poisson structures. https://arxiv.org/abs/1706.02623

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