Affine structures on three-step nilpotent Lie algebras
Abstract: As part of the investigation of the parallel between solvable Lie theory and the theory of groups of affine motions, it is proved that every three-step nilpotent Lie algebra admits a faithful representation of a certain special kind. It follows immediately that every three-step nilpotent Lie group which is connected, simply connected, and of dimension admits a representation as a simply transitive group of affine motions of .
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