International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 2, Pages 71-77
Noncomplete affine structures on Lie algebras of maximal class
Faculté des Sciences et Techniques, 4, Rue des Frères Lumière, Mulhouse Cedex F. 68093, France
Received 29 January 2001
Copyright © 2002 E. Remm and Michel Goze. 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.
Every affine structure on Lie algebra defines a
representation of in . If 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 . As a consequence we give a nonnilpotent faithful linear representation of the 3-dimensional Heisenberg algebra.