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On the integration of Manin pairs
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Paper
On the integration of Manin pairs
2024
Overview
It is a remarkable fact that the integrability of a Poisson manifold to a symplectic groupoid depends only on the integrability of its cotangent Lie algebroid \\(A\\): The source-simply connected Lie groupoid \\(G M\\) integrating \\(A\\) automatically acquires a multiplicative symplectic 2-form. More generally, a similar result holds for the integration of Lie bialgebroids to Poisson groupoids, as well as in the `quasi' settings of Dirac structures and quasi-Lie bialgebroids. In this article, we will place these results into a general context of Manin pairs \\((E,A)\\), thereby obtaining a simple geometric approach to these integration results. We also clarify the case where the groupoid \\(G\\) integrating \\(A\\) is not source-simply connected. Furthermore, we obtain a description of Hamiltonian spaces for Poisson groupoids and quasi-symplectic groupoids within this formalism.
Publisher
Cornell University Library, arXiv.org
Subject
