标题： 八元数对 Clifford 代数的表示和三重性 显示英文标题

标题： Octonionic representations of Clifford algebras and triality

摘要： 克利福德代数表示理论被扩展，以使用八元数或凯莱数的除法代数。 特别是，从该除法代数的非结合性和非交换性中出现的问题得到了解答。 八元数对克利福德代数的表示导致了八元数旋量的概念，并用于给出相应正交群的八元数表示。 最后，显示在这一框架中，三重性自同构表现出明显的$\perm_3 \times SO(8)$结构。 显示英文摘要

摘要： 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.