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On quantum and classical Poisson algebras

100%

Grabowski J., Poncin N.

Banach Center Publications

2007

tom 76

nr 1

313-324

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.

Lie algebraic characterization of manifolds

100%

Grabowski J., Poncin N.

Open Mathematics

2004

tom 2

nr 5

811-825

Results on characterization of manifolds in terms of certain Lie algebras growing on them, especially Lie algebras of differential operators, are reviewed and extended. In particular, we prove that a smooth (real-analytic, Stein) manifold is characterized by the corresponding Lie algebra of linear differential operators, i.e. isomorphisms of such Lie algebras are induced by the appropriate class of diffeomorphisms of the underlying manifolds.

Ograniczanie wyników

1 Banach Center Publications

1 Open Mathematics

2 Grabowski J.

2 Poncin N.

1 2007

1 2004

Wyniki wyszukiwania

On quantum and classical Poisson algebras

Lie algebraic characterization of manifolds