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.
Cite this article
Damien Calaque, A PBW theorem for inclusions of (sheaves of) Lie algebroids. Rend. Sem. Mat. Univ. Padova 131 (2014), pp. 23–47DOI 10.4171/RSMUP/131-3