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.
@article{bwmeta1.element.doi-10_2478_BF02475979,
author = {Janusz Grabowski and Norbert Poncin},
title = {Lie algebraic characterization of manifolds},
journal = {Open Mathematics},
volume = {2},
year = {2004},
pages = {811-825},
zbl = {1138.53313},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02475979}
}
Janusz Grabowski; Norbert Poncin. Lie algebraic characterization of manifolds. Open Mathematics, Tome 2 (2004) pp. 811-825. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02475979/
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