منابع مشابه
Some properties of nilpotent Lie algebras
In this article, using the definitions of central series and nilpotency in the Lie algebras, we give some results similar to the works of Hulse and Lennox in 1976 and Hekster in 1986. Finally we will prove that every non trivial ideal of a nilpotent Lie algebra nontrivially intersects with the centre of Lie algebra, which is similar to Philip Hall's result in the group theory.
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In this note, we consider degenerations between complex 2-step nilpotent Lie algebras of dimension 7 within the variety N 2 7 . This allows us to obtain the rigid algebras in N 2 7 , whose closures give the irreducible components of the variety.
متن کاملDegenerations of nilpotent Lie algebras
In this paper we study degenerations of nilpotent Lie algebras. If λ, μ are two points in the variety of nilpotent Lie algebras, then λ is said to degenerate to μ , λ→deg μ , if μ lies in the Zariski closure of the orbit of λ . It is known that all degenerations of nilpotent Lie algebras of dimension n < 7 can be realized via a one-parameter subgroup. We construct degenerations between characte...
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Assume that $(N,L)$, is a pair of finite dimensional nilpotent Lie algebras, in which $L$ is non-abelian and $N$ is an ideal in $L$ and also $mathcal{M}(N,L)$ is the Schur multiplier of the pair $(N,L)$. Motivated by characterization of the pairs $(N,L)$ of finite dimensional nilpotent Lie algebras by their Schur multipliers (Arabyani, et al. 2014) we prove some properties of a pair of nilpoten...
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In other words, we want to write the corresponding trajectory t → x(t) in closed form. Of course, since this cannot be done for most differential equations, it is important to find a means of approximating a general flow by a flow which is explicitly integrable in closed form. In this paper we describe an infinite dimensional family of explicitly integrable flows E; in a companion paper [6] we ...
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ژورنال
عنوان ژورنال: Georgian Mathematical Journal
سال: 2015
ISSN: 1072-947X,1572-9176
DOI: 10.1515/gmj-2015-0022