Displaying similar documents to “Solvable extensions of a special class of nilpotent Lie algebras”

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.

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...

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

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 p 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...