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Matrix representation of octonions and generalizations

journal contribution
posted on 2023-05-16, 11:49 authored by Daboul, J, Robert DelbourgoRobert Delbourgo
We define a special matrix multiplication among a special subset of 2N×2N matrices, and study the resulting (nonassociative) algebras and their subalgebras. We derive the conditions under which these algebras become alternative nonassociative, and when they become associative. In particular, these algebras yield special matrix representations of octonions and complex numbers; they naturally lead to the Cayley-Dickson doubling process. Our matrix representation of octonions also yields elegant insights into Dirac's equation for a free particle. A few other results and remarks arise as byproducts. © 1999 American Institute of Physics.

History

Publication title

Journal of Mathematical Physics

Volume

40

Issue

8

Pagination

4134-4150

ISSN

0022-2488

Department/School

School of Natural Sciences

Publisher

American Institute of Physics

Place of publication

Melville, NY

Repository Status

  • Restricted

Socio-economic Objectives

Expanding knowledge in the physical sciences

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