Noncomplete affine structures on Lie algebras of maximal class

Noncomplete affine structures on Lie algebras of maximal class

Every affine structure on Lie algebra 𝔤 defines a representation of 𝔤 in aff(ℝn). If 𝔤 is a nilpotent Lie algebra provided with a complete affine structure then the corresponding representation is nilpotent. We describe noncomplete affine structures on the filiform Lie algebra Ln. As a consequence w...

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Main Authors: E. Remm, Michel Goze
Format: Article
Language:English
Published: Hindawi Limited 2002-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/S0161171202011705
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spelling doaj-ededb29b0e7b42cd84b75656c459c91d2020-11-24T21:21:08ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-01292717710.1155/S0161171202011705Noncomplete affine structures on Lie algebras of maximal classE. Remm0Michel Goze1Faculté des Sciences et Techniques, 4, Rue des Frères Lumière, Mulhouse Cedex F. 68093, FranceFaculté des Sciences et Techniques, 4, Rue des Frères Lumière, Mulhouse Cedex F. 68093, FranceEvery affine structure on Lie algebra 𝔤 defines a representation of 𝔤 in aff(ℝn). If 𝔤 is a nilpotent Lie algebra provided with a complete affine structure then the corresponding representation is nilpotent. We describe noncomplete affine structures on the filiform Lie algebra Ln. As a consequence we give a nonnilpotent faithful linear representation of the 3-dimensional Heisenberg algebra.http://dx.doi.org/10.1155/S0161171202011705
collection DOAJ
language English
format Article
sources DOAJ
author E. Remm
Michel Goze
spellingShingle E. Remm
Michel Goze
Noncomplete affine structures on Lie algebras of maximal class
International Journal of Mathematics and Mathematical Sciences
author_facet E. Remm
Michel Goze
author_sort E. Remm
title Noncomplete affine structures on Lie algebras of maximal class
title_short Noncomplete affine structures on Lie algebras of maximal class
title_full Noncomplete affine structures on Lie algebras of maximal class
title_fullStr Noncomplete affine structures on Lie algebras of maximal class
title_full_unstemmed Noncomplete affine structures on Lie algebras of maximal class
title_sort noncomplete affine structures on lie algebras of maximal class
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2002-01-01
description Every affine structure on Lie algebra 𝔤 defines a representation of 𝔤 in aff(ℝn). If 𝔤 is a nilpotent Lie algebra provided with a complete affine structure then the corresponding representation is nilpotent. We describe noncomplete affine structures on the filiform Lie algebra Ln. As a consequence we give a nonnilpotent faithful linear representation of the 3-dimensional Heisenberg algebra.
url http://dx.doi.org/10.1155/S0161171202011705
work_keys_str_mv AT eremm noncompleteaffinestructuresonliealgebrasofmaximalclass
AT michelgoze noncompleteaffinestructuresonliealgebrasofmaximalclass
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