English

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 I2I^2 is an ideal whenever II is an ideal, then this variety coincides with the variety of all Lie algebras.

Keywords

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