Lie algebraic characterization of manifolds

Janusz Grabowski; Norbert Poncin

Open Mathematics (2004)

  • Volume: 2, Issue: 5, page 811-825
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Janusz Grabowski, and Norbert Poncin. "Lie algebraic characterization of manifolds." Open Mathematics 2.5 (2004): 811-825. <http://eudml.org/doc/268851>.

@article{JanuszGrabowski2004,
abstract = {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.},
author = {Janusz Grabowski, Norbert Poncin},
journal = {Open Mathematics},
keywords = {17B63; 13N10; 16S32; 17B40; 17B65; 53D17},
language = {eng},
number = {5},
pages = {811-825},
title = {Lie algebraic characterization of manifolds},
url = {http://eudml.org/doc/268851},
volume = {2},
year = {2004},
}

TY - JOUR
AU - Janusz Grabowski
AU - Norbert Poncin
TI - Lie algebraic characterization of manifolds
JO - Open Mathematics
PY - 2004
VL - 2
IS - 5
SP - 811
EP - 825
AB - 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.
LA - eng
KW - 17B63; 13N10; 16S32; 17B40; 17B65; 53D17
UR - http://eudml.org/doc/268851
ER -

References

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