Parafree metabelian Lie algebras which are determined by parafree Lie algebras

2018 Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics  
Let L be a Lie algebra. Denote by k (L) the k-th term of the derived series of L and by 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= k (P ))= w (P= 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.
doi:10.31801/cfsuasmas.485878 fatcat:ggjdi36yyzbu3bp4ki75qddvce