Octonionic representations of Clifford Algebras and triality
- Oregon State Univ., Corvalis, OR (United States)
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 {Sigma}{sub 3}x SO(8) structure in this framework.
- Sponsoring Organization:
- USDOE
- OSTI ID:
- 272752
- Journal Information:
- Foundations of Physics, Journal Name: Foundations of Physics Journal Issue: 1 Vol. 26; ISSN FNDPA4; ISSN 0015-9018
- Country of Publication:
- United States
- Language:
- English
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