On a problem by Nathan Jacobson for Malcev algebras

Abstract

In this paper we solve a problem for a certain class of Malcev algebras, which is an analogous of an old problem posed by Nathan Jacobson for alternative algebras. Specifically we prove a coordinatization theorem for a class of Malcev algebras containing the 3-dimensional simple Lie algebra ${\mathfrak{sl}}_2(\mathbb{F})$ such that $m{\mathfrak{sl}}_2(\mathbb{F})\ne 0$ for any $0\ne m\in \mathcal{M}.$ We drop the last condition and we describe the structure of the same class of Malcev algebras $\mathcal{M}$ that contains ${\mathfrak{sl}}_2(\mathbb{F})$.

arXiv commentarXiv admin note: text overlap with arXiv:2103.04334