Malcev algebras corresponding to smooth Almost Left Automorphic Moufang Loops

TL;DR

This paper introduces the concept of almost left automorphic Moufang loops and investigates the properties of their tangent algebras in the context of smooth loops.

Contribution

It defines a new class of Moufang loops and analyzes the structure of their tangent algebras, expanding the understanding of loop theory.

Findings

Characterization of tangent algebras for smooth almost left automorphic Moufang loops

Identification of algebraic properties unique to this class

Foundation for further research in loop and algebra theory

Abstract

In this note we introduce the concept of an almost left automorphic Moufang loop and study the properties of tangent algebras of smooth loops of this class.