Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On ideals of free and free nilpotent Lie algebras

Author: Melih Boral
Journal: Proc. Amer. Math. Soc. 94 (1985), 23-28
MSC: Primary 17B65
MathSciNet review: 781048
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Abstract: It is proved that in a free nilpotent Lie algebra there are no nonabelian ideals which are free nilpotent as subalgebras. It is also shown that, for any proper ideal $ S$ of a free Lie algebra $ F$, the quotient of the lower central terms $ {F_m}/{S_m}$ is not finitely generated when $ F \ne {F_2} + S$. If $ F = {F_2} + S,\;F/S$ is finite-dimensional and $ S$ is finitely generated as an ideal in $ F$, then $ {F_m}/{S_m}$ is finitely generated as an algebra for all $ m \geqslant 1$.

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Keywords: Free Lie algebras, ideals, free nilpotent subalgebras, quotients of lower terms
Article copyright: © Copyright 1985 American Mathematical Society