A characterisation of Lie algebras using ideals and subalgebras

Abstract

We prove that if, for a nontrivial variety of non-associative algebras, every subalgebra of every free algebra is free and $I^2$ is an ideal whenever $I$ is an ideal, then this variety coincides with the variety of all Lie algebras.

15 pages, comments are welcome. arXiv admin note: substantial text overlap with arXiv:2205.05364

References in corpus (1)

• An effective criterion for Nielsen-Schreier varieties

Cited by in corpus (1)

• Weak representability of actions of non-associative algebras