On a problem by Nathan Jacobson for Malcev algebras

2021/06/02 by Solís, Victor H. López
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2106.01155

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 \mathfraks l₂(\mathbbF) such that m \mathfraks l₂(\mathbbF)≠ 0 for any 0≠ m\inM. We drop the last condition and we describe the structure of the same class of Malcev algebras M that contains \mathfraks l₂(\mathbbF).

Related

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• Lie algebras with S3 or S4-action, and generalized Malcev algebras
• The simple non-Lie Malcev algebra as a Lie-Yamaguti algebra
• Splitting of operations for alternative and Malcev structures
• Kronecker factorization theorems for the exceptional Malcev algebra