Integrability of Poisson-Lie group actions

Rui Loja Fernandes; David Iglesias Ponte

doi:10.1007/s11005-009-0348-x

Integrability of Poisson-Lie group actions

Rui Loja Fernandes, David Iglesias Ponte

Research output: Contribution to journal › Article › peer-review

Abstract

We establish a 1:1 correspondence between Poisson-Lie group actions on integrable Poisson manifolds and twisted multiplicative Hamiltonian actions on source 1-connected symplectic groupoids. For an action of a Poisson-Lie group G on a Poisson manifold M, we find an explicit description of the lifted Hamiltonian action on the symplectic groupoid Σ(M). We give applications of these results to the integration of Poisson quotients M/G, Lu-Weinstein quotients μ^-1(e)/G and Poisson homogeneous spaces G/H.

Original language	English (US)
Pages (from-to)	137-159
Number of pages	23
Journal	Letters in Mathematical Physics
Volume	90
Issue number	1
DOIs	https://doi.org/10.1007/s11005-009-0348-x
State	Published - Nov 2009
Externally published	Yes

Keywords

Integrability
Poisson actions
Twisted multiplicative

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

Online availability

10.1007/s11005-009-0348-x

Library availability

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keywords = "Integrability, Poisson actions, Twisted multiplicative",

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N2 - We establish a 1:1 correspondence between Poisson-Lie group actions on integrable Poisson manifolds and twisted multiplicative Hamiltonian actions on source 1-connected symplectic groupoids. For an action of a Poisson-Lie group G on a Poisson manifold M, we find an explicit description of the lifted Hamiltonian action on the symplectic groupoid Σ(M). We give applications of these results to the integration of Poisson quotients M/G, Lu-Weinstein quotients μ-1(e)/G and Poisson homogeneous spaces G/H.

AB - We establish a 1:1 correspondence between Poisson-Lie group actions on integrable Poisson manifolds and twisted multiplicative Hamiltonian actions on source 1-connected symplectic groupoids. For an action of a Poisson-Lie group G on a Poisson manifold M, we find an explicit description of the lifted Hamiltonian action on the symplectic groupoid Σ(M). We give applications of these results to the integration of Poisson quotients M/G, Lu-Weinstein quotients μ-1(e)/G and Poisson homogeneous spaces G/H.

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KW - Twisted multiplicative

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Integrability of Poisson-Lie group actions

Abstract

Keywords

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