Parafree metabelian Lie algebras which are determined by parafree Lie algebras

Year 2019, Volume: 68 Issue: 1, 883 - 888, 01.02.2019

Zehra Velioğlu

https://doi.org/10.31801/cfsuasmas.485878

Cited By: 1

Abstract

Let L be a Lie algebra. Denote by δ^{k}(L) the k-th term of the derived series of L and by Δ_{w}(L) the intersection of the ideals I of L such that L/I is nilpotent. We prove that if P is a parafree Lie algebra, then the algebra Q=(P/δ^{k}(P))/Δ_{w}(P/δ^{k}(P)), k≥2 is a parafree solvable Lie algebra. Moreover we show that if Q is not free metabelian, then P is not free solvable for k=2.

Keywords

Parafree Lie algebras, metabelian Lie algebras, solvable Lie algebras

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