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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| Format: | Article |
| Language: | English |
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Wiley
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202011705 |
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| _version_ | 1850165659955101696 |
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| author | E. Remm Michel Goze |
| author_facet | E. Remm Michel Goze |
| author_sort | E. Remm |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-ededb29b0e7b42cd84b75656c459c91d |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-ededb29b0e7b42cd84b75656c459c91d2025-08-20T02:21:41ZengWileyInternational 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 |
| spellingShingle | E. Remm Michel Goze Noncomplete affine structures on Lie algebras of maximal class International Journal of Mathematics and Mathematical Sciences |
| title | 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_short | Noncomplete affine structures on Lie algebras of maximal class |
| title_sort | noncomplete affine structures on lie algebras of maximal class |
| url | http://dx.doi.org/10.1155/S0161171202011705 |
| work_keys_str_mv | AT eremm noncompleteaffinestructuresonliealgebrasofmaximalclass AT michelgoze noncompleteaffinestructuresonliealgebrasofmaximalclass |