Octonionic representations of <i>GL</i>(8,ℛ) and <i>GL</i>(4,𝒞)

Abstract

Octonionic algebra being nonassociative is difficult to manipulate. We introduce left/right octonionic barred operators which enable us to reproduce the associative GL(8,ℛ) group. Extracting the basis of GL(4,𝒞), we establish an interesting connection between the structure of left/right octonionic barred operators and generic 4×4 complex matrices. As an application we give an octonionic representation of the four-dimensional Clifford algebra.