The Ring Division Self Duality

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.