Universal lifting theorem and quasi-Poisson groupoids
| dc.creator | Ponte, David Iglesias | |
| dc.creator | Laurent-Gengoux, Camille | |
| dc.creator | Xu, Ping | |
| dc.date | 2005-07-19 | |
| dc.date.accessioned | 2026-07-07T05:21:51Z | |
| dc.date.available | 2026-07-07T05:21:51Z | |
| dc.description | We 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.description | 46 pages | |
| dc.identifier | https://arxiv.org/abs/math/0507396 | |
| dc.identifier | http://arxiv.org/abs/math/0507396 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75840 | |
| dc.subject | Differential Geometry | |
| dc.subject | 17B66; 22A22; 53D17, 58H05 | |
| dc.title | Universal lifting theorem and quasi-Poisson groupoids | |
| dc.type | text |