Geodesic
Universal lifting theorem and quasi-Poisson groupoids
Journal of the European Mathematical Society, Tome 14 (2012) no. 3, pp. 681-731

Voir la notice de l'article provenant de la source EMS Press

We prove the universal lifting theorem: for an α-simply connected and α-connected Lie groupoid Γ with Lie algebroid A, the graded Lie algebra of multi-differentials on A is isomorphic to that of multiplicative multi-vector fields on Γ. As a consequence, we obtain the integration theorem for a quasi-Lie bialgebroid, which generalizes various integration theorems in the literature in special cases. The second goal of the paper is the study of basic properties of quasi-Poisson groupoids. In particular, we prove that a group pair (D,G) associated to a Manin quasi-triple (d,g,h) induces a quasi-Poisson groupoid on the transformation groupoid G×D/G⇉D/G. Its momentum map corresponds exactly with the D/G-momentum map of Alekseev and Kosmann-Schwarzbach.
DOI : 10.4171/jems/315
Classification : 58-XX, 53-XX, 00-XX
Keywords: Lie algebroids and groupoids, multiplicative multivector fields, Lie bialgebroids, Poisson and symplectic groupoids, Manin pairs, Hamiltonian spaces 
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     title = {Universal lifting theorem and {quasi-Poisson} groupoids},
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David Iglesias-Ponte; Camille Laurent-Gengoux; Ping Xu. Universal lifting theorem and quasi-Poisson groupoids. Journal of the European Mathematical Society, Tome 14 (2012) no. 3, pp. 681-731. doi: 10.4171/jems/315

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