Octonionic Representations of GL(8,R) and GL(4,C)
High Energy Physics - Theory
2009-10-30 v2
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 4x4 complex matrices. As an application we give an octonionic representation of the 4-dimensional Clifford algebra.
Cite
@article{arxiv.hep-th/9607140,
title = {Octonionic Representations of GL(8,R) and GL(4,C)},
author = {Stefano De Leo and Khaled Abdel-Khalek},
journal= {arXiv preprint arXiv:hep-th/9607140},
year = {2009}
}
Comments
14 pages, Revtex, J. Math. Phys. (submitted)