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Octonionic representations of Clifford algebras and triality

Research paper by Jörg Schray, Corinne A. Manogue

Indexed on: 27 Jul '94Published on: 27 Jul '94Published in: High Energy Physics - Theory



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.