Universal lifting theorem and quasi-Poisson groupoids

dc.creatorPonte, David Iglesias
dc.creatorLaurent-Gengoux, Camille
dc.creatorXu, Ping
dc.date2005-07-19
dc.date.accessioned2026-07-07T05:21:51Z
dc.date.available2026-07-07T05:21:51Z
dc.descriptionWe prove the universal lifting theorem: for an $α$-simply connected and $α$-connected Lie groupoid $\gm$ with Lie algebroid $A$, the graded Lie algebra of multi-differentials on $A$ is isomorphic to that of multiplicative multi-vector fields on $\gm$. 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 $(\mathfrak d, \mathfrak g, \mathfrak h)$ induces a quasi-Poisson groupoid on the transformation groupoid $G\times D/G\toto D/G$. Its momentum map corresponds exactly with the $D/G$-momentum map of Alekseev and Kosmann-Schwarzbach.
dc.description46 pages
dc.identifierhttps://arxiv.org/abs/math/0507396
dc.identifierhttp://arxiv.org/abs/math/0507396
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75840
dc.subjectDifferential Geometry
dc.subject17B66; 22A22; 53D17, 58H05
dc.titleUniversal lifting theorem and quasi-Poisson groupoids
dc.typetext

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