TY  - JOUR
T1  - Parafree metabelian Lie algebras which are determined by parafree Lie algebras
AU  - Velioğlu, Zehra
PY  - 2019
DA  - February
Y2  - 2018
DO  - 10.31801/cfsuasmas.485878
JF  - Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics
JO  - Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.
PB  - Ankara University
WT  - DergiPark
SN  - 1303-5991
SP  - 883
EP  - 888
VL  - 68
IS  - 1
LA  - en
AB  - 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.
KW  - Parafree Lie algebras
KW  - metabelian Lie algebras
KW  - solvable Lie algebras
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UR  - https://doi.org/10.31801/cfsuasmas.485878
L1  - https://dergipark.org.tr/en/download/article-file/578275
ER  -