Libor Šnobl (2011)
Archivum Mathematicum
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It is already known that any filiform Lie algebra which possesses a codimension 2 solvable extension is naturally graded. Here we present an alternative derivation of this result.
José M. Ancochea, Rutwig Campoamor (2001)
Extracta Mathematicae
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Campoamor Stursberg, O.R. (2002)
Acta Mathematica Universitatis Comenianae. New Series
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Baoling Guan, Liangyun Chen, Yao Ma (2014)
Czechoslovak Mathematical Journal
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The paper studies nilpotent -Lie superalgebras over a field of characteristic zero. More specifically speaking, we prove Engel’s theorem for -Lie superalgebras which is a generalization of those for -Lie algebras and Lie superalgebras. In addition, as an application of Engel’s theorem, we give some properties of nilpotent -Lie superalgebras and obtain several sufficient conditions for an -Lie superalgebra to be nilpotent by using the notions of the maximal subalgebra, the weak ideal...
Grozman, P., Leites, D., Poletaeva, E. (2002)
Homology, Homotopy and Applications
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B. Es Saadi, Yu. Khakimdjanov, A. Makhlouf (2003)
Annales mathématiques Blaise Pascal
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The aim of this work is to enumerate the standard subalgebras of a semisimple Lie algebra. The computations are based on the approach developed by Yu. Khakimdjanov in 1974. In this paper, we give a general formula for the number of standard subalgebras not necessarly nilpotent of a semisimple Lie algebra of type A and the exceptional semisimple Lie algebras. With computer aided, we enumerate this number for the other types of small rank. Therefore, We deduce the number in the nilpotent...
Elisabeth Remm, Michel Goze (2002)
Revista Matemática Complutense
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We study the class of matrix controlled systems associated to graded filiform nilpotent Lie algebras. This generalizes the non- linear system corresponding to the control of the trails pulled by car.