Moufang symmetry II. Moufang-Mal'tsev pairs and triality

TL;DR

This paper introduces Moufang-Malt'tsev pairs derived from generalized Maurer-Cartan equations, explores their triality property, and constructs the Yamagutian, analyzing its properties within Moufang loops.

Contribution

It presents the concept of Moufang-Malt'tsev pairs and demonstrates how triality underpins their structure, advancing the understanding of Moufang loop symmetries.

Findings

Moufang-Malt'tsev pairs are based on generalized Maurer-Cartan equations.

Triality is a fundamental property of these pairs.

The Yamagutian is constructed and its properties are analyzed.

Abstract

A concept of the Moufang-Malt'tsev pair is elaborated. This concept is based on the generalized Maurer-Cartan equations of a local analytic Moufang loop. Triality can be seen as a fundamental property of such pairs. Based on triality, the Yamagutian is constructed. Properties of the Yamagutian are studied.