GÓMEZ MARTÍN , José Ramón

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Universidad del País Vasco 066.163-EA032/98

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Junta de Andalucia, PAICYT y Ministerio de Ciencia y Tecnología BFM 2000-1047

We give, up to isomorphism and in dimension 8, all the 3-filiform Lie algebras (whose Goze's invariant is (n - 3,1,1,1))..

In this paper, we characterize those Complex Filiform Lie Algeoras of dimension 0 which are derived from other Solvable Lie ALgebras of higher dimensions. This result and the previous one given in ({0]) allow us to lind a complete list of Characteristically Nilpotent Filiform Lie Algebras of dimension 0.

We show a method to determine the space of derivations of any Lie algebra, and in particular we apply this method to a special class of Lie algebras, those nilpotent with low nilindex. Most calculations have been supported by the software Mathematica 3.0.

Naturally graded nilpotent p-filiform Leibniz algebras are studied for p > n − 4, where n is the dimension of the algebra. Using linear algebra methods we describe the naturally graded (n − 3)-filiform Leibniz algebras.

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Heisenberg algebras are the only Lie algebras (g, [, ]) which verify [g, g] = Z(g) and dim(Z(g)) = 1, where Z denotes the center of the algebra. We classify nilpotent Lie superalgebras that verify the same algebraic conditions in arbitrary finite dimension.We study the geometrical properties with the aid of the software Mathematica.