Analytic Loops and Gauge Fields

TL;DR

This paper investigates linear representations of analytic Moufang loops, establishing their complete reducibility in the semisimple case and linking irreducible representations to self-dual Yang-Mills equations in eight dimensions.

Contribution

It proves the complete reducibility of semisimple analytic Moufang loop representations and classifies their irreducible representations, connecting them to higher-dimensional gauge theories.

Findings

All semisimple analytic Moufang loop representations are completely reducible.

Classified all nonassociative irreducible representations.

Linked representations to (anti-)self-dual Yang-Mills equations in ${f R}^8$.

Abstract

In this paper the linear representations of analytic Moufang loops are investigated. We prove that every representation of semisimple analytic Moufang loop is completely reducible and find all nonassociative irreducible representations. We show that such representations are closely associated with the (anti-)self-dual Yang-Mills equations in ${\bf R}^8$