Noncomplete affine structures on Lie algebras of maximal class

E. Remm and Michel Goze

International Journal of Mathematics and Mathematical Sciences, 2002, vol. 29, 1-7

Abstract:

Every affine structure on Lie algebra 𝔤 defines a representation of 𝔤 in aff ( ℝ 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 L n . As a consequence we give a nonnilpotent faithful linear representation of the 3-dimensional Heisenberg algebra.

Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:217345

DOI: 10.1155/S0161171202011705

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