  Results on derivations and automorphisms of some quantum and classical
Poisson algebras, as well as characterizations of manifolds by the Lie
structure of such algebras, are revisited and extended. We prove in particular
somehow unexpected fact that the algebras of linear differential operators
acting on smooth sections of two real vector bundles of rank 1 are isomorphic
as Lie algebras if and only if the base manifolds are diffeomorphic,
independently whether the line bundles themselves are isomorphic or not.
