Moufang symmetry XII. Reductivity and hidden associativity of infinitesimal Moufang transformations

TL;DR

This paper explores the mathematical structure of Moufang transformations, linking their integrability to reductivity conditions and specific algebraic identities, thereby revealing hidden associativity properties.

Contribution

It establishes a connection between the integrability of Moufang transformations and reductivity conditions, introducing new insights into their algebraic structure.

Findings

Integrability of Moufang transformations relates to reductivity conditions.

The Sagle-Yamaguti identity plays a key role in this relationship.

Reveals hidden associativity in the structure of Moufang transformations.

Abstract

It is shown how integrability of the generalized Lie equations of continous Moufang transformatiosn is related to the reductivity conditions and Sagle-Yamaguti identity.