On quantum and classical Poisson algebras
Tom 76 / 2007
Banach Center Publications 76 (2007), 313-324 MSC: Primary 17B63; Secondary 13N10, 16S32, 17B40, 17B65, 53D17. DOI: 10.4064/bc76-0-15
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 a somewhat 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, whether or not the line bundles themselves are isomorphic.