On montre qu’une 2-forme non nulle sur une variété , telle que le pseudogroupe des difféomorphismes locaux la préservant soit transitif sur le fibré des directions tangentes, est symplectique si la dimension de n’est pas . De plus, il y a un contre-exemple en dimension 6, dont on montre qu’il est essentiellement unique.
We prove the universal lifting theorem: for an -simply connected and -connected Lie groupoid with Lie algebroid , the graded Lie algebra of multi-differentials on is isomorphic to that of multiplicative multi-vector fields on . 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,...
The aim of this article is to show that systems of linear partial differential equations on filtered manifolds, which are of weighted finite type, can be canonically rewritten as first order systems of a certain type. This leads immediately to obstructions to the existence of solutions. Moreover, we will deduce that the solution space of such equations is always finite dimensional.