On quantum and classical Poisson algebras

Details On quantum and classical Poisson algebras On quantum and classical Poisson algebras

2005-10-03

arxiv.org/abs/math/0510031v1

Banach Center Publ. 76, Warszawa 2007, 313--324

Mathematics

Differential Geometry

13 pages

Scientific paper

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.

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