用理想和子代数描述李代数的特征

IF 0.8 3区数学 Q2 MATHEMATICS Bulletin of the London Mathematical Society Pub Date : 2024-05-08 DOI:10.1112/blms.13062

Vladimir Dotsenko, Xabier García-Martínez

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引用次数: 0

摘要

我们证明，如果对于一个非偶联代数的非偶联种类，每个自由代数的每个子代数都是自由的，并且 I 2 $I^2$ 是一个理想，只要 I $I$ 是一个理想，那么这个种类就与所有李代数的种类重合。

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A characterisation of Lie algebras using ideals and subalgebras

We prove that if, for a non-trivial 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.