Abstract

It is shown that a central extension of a Lie groupoid by an Abelian Lie group A has a principal A-bundle structure and the extended Lie groupoid is classified by an Euler es-class. Then we prove that for a symplectic α-connected, αβ-transversal or α-simply connected groupoid, there exists at most one central S¹-extension, the Euler es-class of which corresponds to the Poisson cohomology class of the Poisson manifold of units.

Authors