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
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.
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