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Matrix representation of octonions and generalizations


Daboul, J and Delbourgo, R, Matrix representation of octonions and generalizations, Journal of Mathematical Physics, 40, (8) pp. 4134-4150. ISSN 0022-2488 (1999) [Refereed Article]

DOI: doi:10.1063/1.532950


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.

Item Details

Item Type:Refereed Article
Research Division:Physical Sciences
Research Group:Other physical sciences
Research Field:Other physical sciences not elsewhere classified
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the physical sciences
UTAS Author:Daboul, J (Mr Jamil Daboul)
UTAS Author:Delbourgo, R (Professor Robert Delbourgo)
ID Code:16933
Year Published:1999
Web of Science® Times Cited:20
Deposited By:Physics
Deposited On:1999-08-01
Last Modified:2000-05-30

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