Unitary representations of the Virasoro algebra and a conjecture of Kac
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,...