On ideals of free and free nilpotent Lie algebras
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- by Melih Boral PDF
- Proc. Amer. Math. Soc. 94 (1985), 23-28 Request permission
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 $m \geqslant 1$.References
- Benjamin Baumslag, Free Lie algebras and free groups, J. London Math. Soc. (2) 4 (1971/72), 523–532. MR 297824, DOI 10.1112/jlms/s2-4.3.523
- Marshall Hall Jr., A basis for free Lie rings and higher commutators in free groups, Proc. Amer. Math. Soc. 1 (1950), 575–581. MR 38336, DOI 10.1090/S0002-9939-1950-0038336-7
- A. I. Širšov, Subalgebras of free Lie algebras, Mat. Sbornik N.S. 33(75) (1953), 441–452 (Russian). MR 0059892
- Dennis Spellman, On the respective terms of the lower central series of a free group and a normal subgroup, J. Algebra 31 (1974), 293–304. MR 354872, DOI 10.1016/0021-8693(74)90071-4
Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 94 (1985), 23-28
- MSC: Primary 17B65
- DOI: https://doi.org/10.1090/S0002-9939-1985-0781048-6
- MathSciNet review: 781048