Octonionic Representations of GL(8,R) and GL(4,C)

Details Octonionic Representations of GL(8,R) and GL(4,C) Octonionic Representations of GL(8,R) and GL(4,C)

1996-07-17

arxiv.org/abs/hep-th/9607140v2

J.Math.Phys. 38 (1997) 582-598

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, Revtex, J. Math. Phys. (submitted)

Scientific paper

10.1063/1.531879

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.

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