IJPAM: Volume 95, No. 4 (2014)

PRIMITIVE ELEMENTS AND PREIMAGE OF
PRIMITIVE SETS OF FREE LIE ALGEBRAS

Dilek Ersalan$^1$, Zerrin Esmerligil$^2$
$^{1,2}$Department of Mathematics
Cukurova University
Adana, TURKEY


Abstract. Let $F$ and $L$ be free Lie algebras of finite rank $n$ and $m$ respectively and $\phi $ be a homomorphism from $F$ to $L$. We prove that the preimage of a primitive set of $L$ contains a primitive set of $F$. As a consequence of this result we obtain that an element $h$ of a subalgebra $H$ of $F$ is primitive in $H$ if it is primitive in $F$.

Also we show that in a free Lie algebra of the form $F/\gamma _{m+1}\left( R\right) $ if the ideal $\left\langle g\right\rangle _{id}$ of this algebra contains a primitive element $h$ then $h$ and $g$ are conjugate by means of an inner automorphism.

Received: April 11, 2014

AMS Subject Classification: 17B01, 17B40

Key Words and Phrases: primitive element, free Lie algebra

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DOI: 10.12732/ijpam.v95i4.5 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: 2014
Volume: 95
Issue: 4
Pages: 535 -


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