A PBW theorem for inclusions of (sheaves of) Lie algebroids (Q396481)

This paper is a step towards the project to construct a dictionary between Lie theory and algebraic geometry. The author first recalls the definitions and basic properties of the universal enveloping algebra, the de Rham complex and jets of a Lie algebroid. The Chen-Stienon-Xu class is then interpreted as an obstruction for extending modules to the first infinitesimal neighbourhood. A Poincaré-Birkhoff-Witt (PWB) theorem is then proved. To this end, the author uses straightforward generalizations of tools developed by Caldararu and Tu.