On the Lie algebra of a Malcev algebra

TL;DR

This paper explores the structure of Malcev algebras by examining their associated Lie algebras, establishing a unique correspondence, and analyzing root-space decompositions to deepen understanding of their ideal structures.

Contribution

It introduces a unique Lie algebra correspondence for Malcev algebras and characterizes their root-space decomposition, advancing structural theory.

Findings

Established a unique Lie algebra correspondence for Malcev algebras

Derived properties of ideals within Malcev algebras

Proved the root-space decomposition structure

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.