Foundations of Physics

, Volume 26, Issue 1, pp 17–70 | Cite as

Octonionic representations of Clifford algebras and triality

  • Jörg Schray
  • Corinne A. Manogue


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 Σ3×SO(8) structure in this framework.


Division Algebra Clifford Algebra Orthogonal Group Cayley Number Triality Automorphism 
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Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • Jörg Schray
    • 1
  • Corinne A. Manogue
    • 1
  1. 1.Department of PhysicsOregon State UniversityCorvalis

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