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

Abstract

Inspired by the recent work of Chen-Stiénon-Xu on Atiyah classes associated to inclusions of Lie algebroids, we give a very simple criterium (in terms of those classes) for relative Poincaré-Birkhoff-Witt type results to hold. The tools we use (e.g. the first infinitesimal neighbourhood Lie algebroid) are straightforward generalizations of the ones previously developped by Caldararu, Tu and the author for Lie algebra inclusions.

Final version - several changes - 19 pages

Cited by in corpus (3)

• Poincaré--Birkhoff--Witt isomorphisms and Kapranov dg-manifolds
• Invariant connections and PBW theorem for Lie groupoid pairs
• Atiyah classes of strongly homotopy Lie pairs