International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2002 / Article

Open Access

Volume 29 |Article ID 217345 | https://doi.org/10.1155/S0161171202011705

E. Remm, Michel Goze, "Noncomplete affine structures on Lie algebras of maximal class", International Journal of Mathematics and Mathematical Sciences, vol. 29, Article ID 217345, 7 pages, 2002. https://doi.org/10.1155/S0161171202011705

Noncomplete affine structures on Lie algebras of maximal class

Received29 Jan 2001

Abstract

Every affine structure on Lie algebra 𝔤 defines a representation of 𝔤 in aff(n). 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.

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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