CHARACTERISTICALLY NILPOTENT LIE ALGEBRAS

The definitions, the first properties, and some examples of characteristically nilpotent Lie algebras have been given in Chapter 2 (see Section III in this chapter). Here we study these algebras from a geometrical point of view, by considering them as points of the variety N n. This study leads us to 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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