Matrix representation of octonions and generalizations
Jun, 199918 pages
Published in:
- J.Math.Phys. 40 (1999) 4134-4150
e-Print:
- hep-th/9906065 [hep-th]
DOI:
Report number:
- UTAS-PHYS-98-25
View in:
Citations per year
Abstract:
We define a special matrix multiplication among a special subset of 2N\x 2N matrices, and study the resulting (non-associative) algebras and their subalgebras. We derive the conditions under which these algebras become alternative non-associative 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.- algebra: octonion
- algebra: representation
- algebra: Lie
References(30)
Figures(0)