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arXiv · 2210.14550

A characterisation of Lie algebras using ideals and subalgebras

Vladimir Dotsenko·Xabier García-Martínez
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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.

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Vladimir Dotsenko, Xabier García-Martínez. 2022-10-26. A characterisation of Lie algebras using ideals and subalgebras. https://doi.org/10.1112/blms.13062

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