Titlebook: Nilpotent Lie Algebras; Michel Goze,Yusupdjan Khakimdjanov Book 1996 Springer Science+Business Media Dordrecht 1996 Cohomology.Grad.algebr

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Applications to Differential Geometry: The Nilmanifolds, are entirely defined in the Lie algebra. This explains why the exceptional examples of affine manifolds, of symplectic compact non-kahlerian manifolds, of naturally reductive Riemaniann manifolds, and the counter examples of Lichnerowicz’s conjecture on the harmonic spaces are described as nilmanifolds.

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Characteristically Nilpotent Lie Algebras, a stupendous result: almost all nilpotent Lie algebras are characteristically nilpotents. Then the determination of the noncharacteristically nilpotents seems natural. We conclude this chapter by giving and describing this family of noncharacteristically nilpotent filiform Lie algebras.

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