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

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 ≥ 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...

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.