Geodesic
On embeddings of some quotient algebras of free sums of Lie algebras
Fundamentalʹnaâ i prikladnaâ matematika, Tome 10 (2004) no. 4, pp. 235-241 
A. L. Shmel'kin; A. V. Syrtsov. On embeddings of some quotient algebras of free sums of Lie algebras. Fundamentalʹnaâ i prikladnaâ matematika, Tome 10 (2004) no. 4, pp. 235-241. http://geodesic.mathdoc.fr/item/FPM_2004_10_4_a14/
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     author = {A. L. Shmel'kin and A. V. Syrtsov},
     title = {On embeddings of some quotient algebras of free sums of {Lie} algebras},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2004_10_4_a14/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $(B_i)_{i\in I}$ be a set of Lie algebras; let $X$ be a free Lie algebra; let $F=\Bigl(\,\mathop{\sum\limits_{i\in I}}\nolimits^{*}B_i\Bigr)*X$ be their free sum; let $R$ be an ideal of $F$ such that $R\cap B_i=1$ ($i\in I$); let $V$ be a variety of Lie algebras such that $\mathbf{V}(R)$ is an ideal of $F$. Under some restrictions, we construct an embedding of $F/\mathbf{V}(R)$ into the verbal wreath product of a free algebra of the variety $V$ with $F/R$.

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