On k-abelian, p-filiform Lie algebras

Details On k-abelian, p-filiform Lie algebras On k-abelian, p-filiform Lie algebras

2000-07-28

arxiv.org/abs/math/0007176v2

Mathematics

Rings and Algebras

22 Latex Pages. Part of the communication given in the I Colloquium of Lie theory celebrated in Vigo 17-22 july 2000

Scientific paper

We classify the (n-5)-filiform Lie algebras which have the additional property of a non-abelian derived subalgebra. We show that this property is strongly related with the structure of the Lie algebra of derivations; explicitely we show that if a (n-5)-filiform algebra is characteristically nilpotent, then it must be 2-abelian. We also give applications of k-abelian Lie algebras to the construction of solvable rigis algebras, as well as to the theory of nilalgebras of parabolic subalgebras in the example of the exceptional simple model E_{6}.

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