Poisson enveloping algebras and the Poincaré-Birkhoff-Witt theorem

Thierry Lambre, Cyrille Ospel, Pol Vanhaecke

Poisson algebras are, just like Lie algebras, particular cases of Lie-Rinehart algebras. The latter were introduced by Rinehart in his seminal 1963 paper, where he also introduces…