The Ring Division Self Duality

TL;DR

This paper introduces an algebraic construction of instantonic equations over octonions, highlighting their relation to quaternionic cases, Clifford algebra, and topological stability, revealing deep geometric and algebraic structures.

Contribution

It provides a novel algebraic formulation of instantonic equations over octonions using Clifford algebra, connecting to topological stability and geometric structures like parallelizable spheres.

Findings

Explicit topological criteria for solution stability

Connection between octonionic instantons and parallelizable spheres

Unified Clifford algebra framework for algebraic and geometric features

Abstract

We present a simple construction of the instantonic type equation over octonions where its similarities and differences with the quaternionic case are very clear. We use the unified language of Clifford Algebra. We argue that our approach is the pure algebraic formulation of the geometric based soft Lie algebra. The topological criteria for the stability of our solution is given explicitly to establish its solitonic property. Many beautiful features of the parallelizable ring division spheres and Absolute Parallelism (AP) reveal their presence in our formulation.