2005/07/19 by David Iglesias Ponte, Ponte, David Iglesias, Camille Laurent-Gengoux +3 · 1 citation
Mathematics · #17B66 #22A22 #53D17 #58H05 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.DG #msc:17B66 #msc:22A22 #msc:53D17 #msc:58H05
paper · pdf · doi:10.48550/arxiv.math/0507396
46 pages
arxiv created 2005/07/19 · openalex publication_date 2005/07/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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× D/G\toto D/G. Its momentum map corresponds exactly with the D/G-momentum map of Alekseev and Kosmann-Schwarzbach.