International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 2, Pages 71-77
doi:10.1155/S0161171202011705
Noncomplete affine structures on Lie algebras of maximal class
E. Remm
and Michel Goze
Faculté des Sciences et Techniques, 4, Rue des Frères Lumière, Mulhouse Cedex F. 68093, France
Abstract
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.