Abstract
We consider the embedding problem of a nilpotent Lie algebra into a stratified one; we construct all nilpotent Lie algebras of dimension ⩽ 7 having a fixed Lie algebra of codimension 1, and we get among other results, a new classification of 6-dimensional nilpotent Lie algebras. This study has applications on the analysis of deformations of the internal space of 11 dimensional Kaluza-Klein theories (non abelian theories) and in 11-dimensional supergravity.
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