On dimension of Lie Algebras and nilpotent Lie algebras

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Arabyani H.

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Journal Paper

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Journal: Mathematics and Computational Sciences Year:2022 | Volume:3 | Issue:1 Page(s): 33-36

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Title

On dimension of Lie Algebras and nilpotent Lie algebras

Author(s)

Arabyani H. | Issue Writer Certificate

Keywords

Nilpotent Lie algebra

Derived subalgebra

Frattini subalgebra

Abstract

Schur proved that if the center of a group G has finite index, then the derived subgroup G′ is also finite. Moneyhun proved that if L is a Lie algebra such that dim(L/Z(L)) = n, then dim(L^2) ≤1/2n(n-1) In this paper, we extend the converse of Moneyhun’s theorem. Also, we prove a wellknown result of Nilpotent Lie algebras by using a different technique

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