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Characteristically nilpotent Lie algebras. (Russian) Zbl 0716.17008

Nilpotent Lie algebras with only nilpotent derivations are studied. Such Lie algebras are called characteristically nilpotent. With the help of deformations of nilpotent graded Lie algebras, over a field of characteristic 0, with maximal index of nilpotency, the author gets a big family of characteristically nilpotent Lie algebras in any finite dimension \(\geq 7\), which include most of the known examples. He shows that in the affine algebraic manifold \(\mathcal N_ n\) of nilpotent Lie algebra structures of dimension \(\geq 12\), there exists a nonempty Zariski open set of characteristically nilpotent Lie algebras. He also proves the existence of an irreducible, locally closed subset of such Lie algebras of \(\mathcal N_ n\) of dimension \(O(n^ 2)\).

MSC:

17B30 Solvable, nilpotent (super)algebras
17B70 Graded Lie (super)algebras
17B56 Cohomology of Lie (super)algebras
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