Matrix representation of octonions and generalizations

被引：25

作者：

Daboul, J ^{[1
]}

Delbourgo, R

机构：

[1] Univ Tasmania, Sch Math & Phys, Hobart, Tas, Australia

[2] Ben Gurion Univ Negev, Dept Phys, IL-84105 Beer Sheva, Israel

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 1999年 / 40卷 / 08期

关键词：

D O I：

10.1063/1.532950

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We define a special matrix multiplication among a special subset of 2Nx2N 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. (C) 1999 American Institute of Physics. [S0022-2488(99)03108-4].

引用

页码：4134 / 4150

页数：17