On quantum and classical Poisson algebras

• Autorzy: Janusz Grabowski , Norbert Poncin
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 17B65: Infinite-dimensional Lie (super)algebras
• 16S32: Rings of differential operators
• 53D17: Poisson manifolds; Poisson groupoids and algebroids
• 17B40: Automorphisms, derivations, other operators
• 13N10: Rings of differential operators and their modules
• 17B63: Poisson algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2007
• Tom: 76
• Numer: 1
• Strony: 313-324

Daty

wydano

2007

Twórcy

autor

Janusz Grabowski

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, P.O. Box 21, 00-956 Warszawa, Poland

autor

Norbert Poncin

• Institute of Mathematics, University of Luxembourg, Avenue de la Faïencerie, 162A, L-1511 Luxembourg City, Grand-Duchy of Luxembourg

Identyfikatory

DOI

10.4064/bc76-0-15