Octonionic representations of Clifford algebras and triality

Details Octonionic representations of Clifford algebras and triality Octonionic representations of Clifford algebras and triality

1994-07-27

arxiv.org/abs/hep-th/9407179v1

Found.Phys.26:17-70,1996

Physics

High Energy Physics

High Energy Physics - Theory

33 pages

Scientific paper

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.

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