Parafree metabelian Lie algebras which are determined by parafree Lie algebras

Authors : Zehra VELİOĞLU

Pages : 883-888

Doi:10.31801/cfsuasmas.485878

View : 16 | Download : 12

Publication Date : 2019-02-01

Article Type : Research Paper

Abstract :Let L be a Lie algebra. Denote by δ^{k}insert ignore into journalissuearticles values(L); the k-th term of the derived series of L and by Δ_{w}insert ignore into journalissuearticles values(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=insert ignore into journalissuearticles values(P/δ^{k}insert ignore into journalissuearticles values(P););/Δ_{w}insert ignore into journalissuearticles values(P/δ^{k}insert ignore into journalissuearticles values(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