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Nilpotent Lie algebras. (English) Zbl 0845.17012
Mathematics and its Applications (Dordrecht). 361. Dordrecht: Kluwer Academic Publishers. xv, 334 p. (1996).
Results on some major classes of nilpotent Lie algebras are presented. Emphasized are filiform Lie algebras, characteristically nilpotent Lie algebras, nilpotent standard algebras and two step nilpotent Lie algebras. The Chevalley cohomology of filiform algebras is discussed as is that of the nilradical of parabolic subalgebras. An extensive study of varieties specializes in the variety of $$n$$-dimensional nilpotent Lie algebra laws where various irreducible components are considered, especially filiform components. The study of characteristically nilpotent Lie algebras culminates in showing that almost all nilpotent Lie algebras are of this type.
The final chapter consists of applications to differential geometry; in particular, to nilmanifolds whose differential calculus is that of linear calculus on the corresponding nilpotent Lie algebra.

##### MSC:
 17B30 Solvable, nilpotent (super)algebras 17-02 Research exposition (monographs, survey articles) pertaining to nonassociative rings and algebras