Some properties of nilpotent Lie algebras

Subject Areas : Statistics

M.R. Rismanchian ¹ (Department of Pure Mathematics, Faculty of Mathematical Sciences, Shahrekord University, Shahrekord, Iran.)
M. Araskhan ² (Department of Mathematic, Yazd - Branch, Islamic Azad University, Yazd, Iran)

Received: 2019-01-04 Accepted : 2019-05-06 Published : 2019-05-01

Keywords: مرکز جبرلی, سری مرکزی, ایده‌آل کمین, موضعاً پوچ توان,

Abstract :

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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