INSTITUTE OF MATHEMATICS · POLISH ACADEMY OF SCIENCES BANACH CENTER PUBLICATIONS ISSN: 0137-6934(p) 1730-6299(e)

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On quantum and classical Poisson algebras

Janusz Grabowski¹, Norbert Poncin²
Banach Center Publ. 76 (2007), 313-324

Abstract: 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.


MSC (2000): Primary 17B63; Secondary 13N10, 16S32, 17B40, 17B65, 53D17.

1. Institute of Mathematics
   Polish Academy of Sciences
   Œniadeckich 8
   P.O. Box 21
   00-956 Warszawa, Poland
   
2. Institute of Mathematics
   University of Luxembourg
   Avenue de la Faiencerie, 162A,
   L-1511 Luxembourg City, Grand-Duchy of Luxembourg
   

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