IJPAM: Volume 105, No. 1 (2015)

THE STRUCTURE OF THE LIE ALGEBRA
$\gamma _{n}(F)/[\gamma _{n}\left(F\right) ,F^{^{\prime }}]$

Dilek Ersalan
Department of Mathematics
Cukurova University
Adana, TURKEY


Abstract. Let $F$ be a free Lie algebra of finite rank.

We show that $\gamma
_{n}(F/F^{^{\prime \prime }})$ is free abelian of infinite rank and the algebra $\gamma _{n}(F)\cap F^{^{\prime \prime }}/[\gamma _{n}\left(
F\right) ,F^{^{\prime }}]$ is finitely generated and then we prove that the algebra $\gamma _{n}(F)/[\gamma _{n}\left(F\right) ,F^{^{\prime }}]$ is infinitely generated.

Moreover, for sufficiently small values of n we show that $\gamma _{n}(F)/[\gamma _{n}\left(F\right) ,F^{^{\prime }}]$ is free abelian.

Received: November 2, 2015

AMS Subject Classification: 17B01

Key Words and Phrases: free abelian Lie algebra, finitely generated Lie algebra, lower central term

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DOI: 10.12732/ijpam.v105i1.11 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 105
Issue: 1
Pages: 127 - 131


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