On the Lie algebra of a Malcev algebra

2024/06/20 by Olufemi O. Oyadare, Oyadare, Olufemi O.
Mathematics · #17B05 #17B22 #17D10 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2406.14592

openalex publication_date 2024/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper develops the structure theory of a Malcev algebra via the consideration of its most important and largest Lie (sub-) algebra. We introduce the notion of a Lie algebra which uniquely corresponds to a Malcev algebra and use this correspondence to derive some basic properties of some types of ideals in the Malcev algebra. We then prove the exact nature of the root-space decomposition of a Malcev algebra.

Related

• On a problem by Nathan Jacobson for Malcev algebras
• The simple non-Lie Malcev algebra as a Lie-Yamaguti algebra
• Splitting of operations for alternative and Malcev structures
• Lie algebras with S3 or S4-action, and generalized Malcev algebras
• A new characterization of Kac-Moody-Malcev superalgebras