Displaying similar documents to “Some necessary and sufficient conditions for nilpotent n -Lie superalgebras”

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...

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...

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.

Ricci-flat left-invariant Lorentzian metrics on 2-step nilpotent Lie groups

Mohammed Guediri, Mona Bin-Asfour (2014)

Archivum Mathematicum

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The purpose of this paper is to investigate Ricci-flatness of left-invariant Lorentzian metrics on 2-step nilpotent Lie groups. We first show that if , is a Ricci-flat left-invariant Lorentzian metric on a 2-step nilpotent Lie group N , then the restriction of , to the center of the Lie algebra of N is degenerate. We then characterize the 2-step nilpotent Lie groups which can be endowed with a Ricci-flat left-invariant Lorentzian metric, and we deduce from this that a Heisenberg Lie group...

A nilpotent Lie algebra and eigenvalue estimates

Jacek Dziubański, Andrzej Hulanicki, Joe Jenkins (1995)

Colloquium Mathematicae

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The aim of this paper is to demonstrate how a fairly simple nilpotent Lie algebra can be used as a tool to study differential operators on ℝ n with polynomial coefficients, especially when the property studied depends only on the degree of the polynomials involved and/or the number of variables.