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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 DelbourgoWe 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 PhysicsVolume
40Issue
8Pagination
4134-4150ISSN
0022-2488Department/School
School of Natural SciencesPublisher
American Institute of PhysicsPlace of publication
Melville, NYRepository Status
- Restricted