Non-Associativity in the Clifford Bundle on the Parallelizable Torsion 7-Sphere

TL;DR

This paper explores the unique non-associative properties of Clifford bundles on the 7-sphere, revealing their impact on spinor transformations and Kac-Moody algebras with potential applications.

Contribution

It introduces new insights into the non-associative structure of Clifford bundles on S7 and their implications for spinor fields and algebraic transformations.

Findings

Demonstrates novel non-associative properties of Clifford bundles on S7

Shows how these properties influence spinor field transformations

Explores consequences for Kac-Moody current algebras

Abstract

In this paper we discuss generalized properties of non-associativity in Clifford bundles on the 7-sphere S7. Novel and prominent properties inherited from the non-associative structure of the Clifford bundle on S7 are demonstrated. They naturally lead to general transformations of the spinor fields on S7 and have dramatic consequences for the associated Kac-Moody current algebras. All additional properties concerning the non-associative structure in the Clifford bundle on S7 are considered. We further discuss and explore their applications.