@article{article_485878, title={Parafree metabelian Lie algebras which are determined by parafree Lie algebras}, journal={Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics}, volume={68}, pages={883–888}, year={2019}, DOI={10.31801/cfsuasmas.485878}, author={Velioğlu, Zehra}, keywords={Parafree Lie algebras,metabelian Lie algebras,solvable Lie algebras}, 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.}, number={1}, publisher={Ankara University}