15 may 2017 -- 14:30
Sala Riunioni DipMat, Salerno
Abstract.
In this talk, we will address the problem of deformations of Lie algebroids. Following an article by Crainic and Moerdijk (2008), we define the deformation complex of a Lie algebroid A as the dgla of multiderivations of A, with a Chevalley-Eilenberg-like differential. We attach to every deformation of A a class in the second cohomology group and we show that it only depends on the equivalence class of the deformation. Then, we relate deformation cohomology of Lie algebroids to known ones, such as Lie algebra cohomology, Poisson cohomology and foliated cohomology. Finally, we state a conjecture (now solved) about the deformation cohomology of Lie algebroids coming from proper Lie groupoids with 2-connected s-fibers.