A characterisation of Lie algebras using ideals and subalgebras
Rings and Algebras
2022-10-27 v1
Abstract
We prove that if, for a nontrivial variety of non-associative algebras, every subalgebra of every free algebra is free and is an ideal whenever is an ideal, then this variety coincides with the variety of all Lie algebras.
Cite
@article{arxiv.2210.14550,
title = {A characterisation of Lie algebras using ideals and subalgebras},
author = {Vladimir Dotsenko and Xabier García-Martínez},
journal= {arXiv preprint arXiv:2210.14550},
year = {2022}
}
Comments
15 pages, comments are welcome. arXiv admin note: substantial text overlap with arXiv:2205.05364