Octonionic representations of Clifford algebras and triality
arXiv:hep-th/9407179 · doi:10.1007/BF02058887
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 non-associativity and non-commutativity of this division algebra are answered. Octonionic representations for Clifford algebras lead to a notion of octonionic spinors and are used to give octonionic representations of the respective orthogonal groups. Finally, the triality automorphisms are shown to exhibit a manifest $\perm_3 \times SO(8)$ structure in this framework.
33 pages
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Cited by in corpus (21)
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