Unified Octonionic Representation of the 10-13 Dimensional Clifford Algebra

TL;DR

This paper introduces a unified octonionic representation for various high-dimensional Clifford algebras using 8x8 real matrices, simplifying their mathematical structure.

Contribution

It provides a novel one-dimensional octonionic framework that unifies multiple high-dimensional Clifford algebras with explicit matrix representations.

Findings

Unified octonionic representation for Cliff(5,5), Cliff(6,6), and Cliff(7,6)

Representation using 8x8 real matrices

Simplifies understanding of high-dimensional Clifford algebras

Abstract

We give a one dimensional octonionic representation of the different Clifford algebra Cliff(5,5)\sim Cliff(9,1), Cliff(6,6)\sim Cliff(10,2) and lastly Cliff(7,6)\sim Cliff(10,3) which can be given by (8x8) real matrices taking into account some suitable manipulation rules.