On embeddings of some quotient algebras of free sums of Lie algebras

Abstract

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