On the free Lie-Yamaguti algebra

TL;DR

This paper describes the structure of the free Lie Yamaguti algebra, which arises naturally in the context of reductive homogeneous spaces and their geometric operators.

Contribution

It provides a detailed algebraic description of the free Lie Yamaguti algebra, a topic not previously fully explored.

Findings

Characterization of the free Lie Yamaguti algebra

Connection to tangent bundle sections of reductive homogeneous spaces

Framework for algebraic operators representing torsion and curvature

Abstract

Lie Yamaguti algebras appear naturally on the smooth sections of the tangent bundle of a reductive homogeneous space when we interpret the torsion and curvature as algebraic operators. In this article we present a description of the free Lie Yamaguti algebra.