On quantum and classical Poisson algebras

Janusz Grabowski, and Norbert Poncin. "On quantum and classical Poisson algebras." Banach Center Publications 76.1 (2007): 313-324. <http://eudml.org/doc/282516>.

@article{JanuszGrabowski2007,
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.},
author = {Janusz Grabowski, Norbert Poncin},
journal = {Banach Center Publications},
keywords = {line bundles; differential operators; derivations; automorphisms; Lie algebras; Chevalley cohomology; one-parameter groups},
language = {eng},
number = {1},
pages = {313-324},
title = {On quantum and classical Poisson algebras},
url = {http://eudml.org/doc/282516},
volume = {76},
year = {2007},
}

TY - JOUR
AU - Janusz Grabowski
AU - Norbert Poncin
TI - On quantum and classical Poisson algebras
JO - Banach Center Publications
PY - 2007
VL - 76
IS - 1
SP - 313
EP - 324
AB - 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.
LA - eng
KW - line bundles; differential operators; derivations; automorphisms; Lie algebras; Chevalley cohomology; one-parameter groups
UR - http://eudml.org/doc/282516
ER -