Octonionic representations of Clifford algebras and triality
Abstract
The theory of representations of Clifford algebras is extended to employ the division algebra of the octonions or Cayley numbers. In particular, questions that arise from the nonassociativity and noncommutativity of this division algebra are answered. Octonionic representations for Clifford algebras lead to a notion of octonionic spinors and are used to give octoninic representations of the respective orthogonal groups. Finally, the triality automorphisms are shown to exhibit a manifest Σ _{3} ×SO(8) structure in this framework.
 Publication:

Foundations of Physics
 Pub Date:
 January 1996
 DOI:
 10.1007/BF02058887
 arXiv:
 arXiv:hepth/9407179
 Bibcode:
 1996FoPh...26...17S
 Keywords:

 High Energy Physics  Theory;
 Mathematics  Quantum Algebra
 EPrint:
 33 pages