A characterisation of Lie algebras using ideals and subalgebras

2022/10/26 by Vladimir Dotsenko, Dotsenko, Vladimir, Xabier García‐Martínez +1
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topics in Algebra #Advanced Topology and Set Theory #FOS: Mathematics #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2210.14550

openalex publication_date 2022/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that if, for a nontrivial variety of non-associative algebras, every subalgebra of every free algebra is free and I² is an ideal whenever I is an ideal, then this variety coincides with the variety of all Lie algebras.

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