Standard Subalgebras of Semisimple Lie Algebras and Computer-Aided for Enumeration

B. Es Saadi; Yu. Khakimdjanov; A. Makhlouf

Displaying similar documents to “Standard Subalgebras of Semisimple Lie Algebras and Computer-Aided for Enumeration”

Characteristically nilpotent Lie Algebras: a survey.

José M. Ancochea, Rutwig Campoamor (2001)

Extracta Mathematicae

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Some necessary and sufficient conditions for nilpotent $n$ -Lie superalgebras

Baoling Guan, Liangyun Chen, Yao Ma (2014)

Czechoslovak Mathematical Journal

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The paper studies nilpotent $n$ -Lie superalgebras over a field of characteristic zero. More specifically speaking, we prove Engel’s theorem for $n$ -Lie superalgebras which is a generalization of those for $n$ -Lie algebras and Lie superalgebras. In addition, as an application of Engel’s theorem, we give some properties of nilpotent $n$ -Lie superalgebras and obtain several sufficient conditions for an $n$ -Lie superalgebra to be nilpotent by using the notions of the maximal subalgebra, the weak ideal...

Solvable extensions of a special class of nilpotent Lie algebras

A. Shabanskaya, Gerard Thompson (2013)

Archivum Mathematicum

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A pair of sequences of nilpotent Lie algebras denoted by $N_{n, 11}$ and $N_{n, 19}$ are introduced. Here $n$ denotes the dimension of the algebras that are defined for $n \geq 6$ ; the first term in the sequences are denoted by 6.11 and 6.19, respectively, in the standard list of six-dimensional Lie algebras. For each of $N_{n, 11}$ and $N_{n, 19}$ all possible solvable extensions are constructed so that $N_{n, 11}$ and $N_{n, 19}$ serve as the nilradical of the corresponding solvable algebras. The construction continues Winternitz’ and colleagues’ program...

On $k$ -filiform Lie algebras. I.

Campoamor Stursberg, O.R. (2002)

Acta Mathematica Universitatis Comenianae. New Series

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Maximal solvable extensions of filiform algebras

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.

Degenerations of nilpotent Lie algebras.

Burde, Dietrich (1999)

Journal of Lie Theory

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Nilpotent control systems.

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.

A computer-based approach to the classification of nilpotent Lie algebras.

Schneider, Csaba (2005)

Experimental Mathematics

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