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Non-filiform characteristically nilpotent and complete Lie algebras

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Ancochea Bermúdez, José María and Campoamor Stursberg, Otto Ruttwig (2002) Non-filiform characteristically nilpotent and complete Lie algebras. Algebra Colloquium, 9 (4). pp. 455-468. ISSN 1005-3867

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Abstract

One of the main achievements of the paper under review is the construction of new classes of characteristically nilpotent Lie algebras that are not filiform. In fact, in
Theorem 4.5 one describes, for arbitrary m 4, a characteristically nilpotent Lie algebra of dimension 2m+ 2 whose characteristic sequence is (2m− 1, 2, 1). The starting point of that construction is given by the Lie algebras denoted by g4(m,m−1). The latter algebra is characterized in Theorem 3.7 as the only naturally graded central extension of L2m−1 by C with nilindex 2m − 1, where L2m−1 is the Lie algebra having a basis {X1, . . . ,X2m} such that [X1,Xi] = Xi+1 for 2 i 2m − 1, and [Xi,Xj ] = 0 for the other pairs of basis vectors. The main idea of the aforementioned construction of non-filifor characteristically nilpotent Lie algebras is to consider deformations of the algebras g4(m,m−1).


Item Type:Article
Uncontrolled Keywords:characteristically nilpotent Lie algebras; complete Lie algebras; rigid Lie algebras
Subjects:Sciences > Mathematics > Algebra
ID Code:20847
Deposited On:15 Apr 2013 14:34
Last Modified:12 Dec 2018 15:13

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