Discussiones Mathematicae General Algebra and Applications 24(2) (2004) 251-265
doi: 10.7151/dmgaa.1088

[BIBTex] [PDF] [PS]

ON THE STRUCTURE AND ZERO DIVISORS OF THE CAYLEY-DICKSON SEDENION ALGEBRA

Raoul E. Cawagas

SciTech R and D Center, OVPRD,
Polytechnic University of the Philippines, Manila

e-mail: raoulec@yahoo.com

Abstract

The algebras C (complex numbers), H (quaternions), and O (octonions) are real division algebras obtained from the real numbers R by a doubling procedure called the Cayley-Dickson Process. By doubling R (dim 1), we obtain C (dim 2), then C produces H (dim 4), and H yields O (dim 8). The next doubling process applied to O then yields an algebra S (dim 16) called the sedenions. This study deals with the subalgebra structure of the sedenion algebra S and its zero divisors. In particular, it shows that S has subalgebras isomorphic to R, C, H, O, and a newly identified algebra [O~] called the quasi-octonions that contains the zero-divisors of S.

Keywords: sedenions, subalgebras, zero divisors, octonions, quasi-octonions, quaternions, Cayley-Dickson process, Fenyves identities.

2000 Mathematics Subject Classification: 20N05, 17A45.

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Received 19 May 2004
Revised 25 July 2004
Revised 30 December 2004