On triality and automorphisms and derivations of composition algebras
Let \((C,q)\) be a Cayley-Dickson algebra over a field \(F\) of arbitrary characteristic with norm \(q\). The author studies automorphisms, derivations and orthogonal transformations of \((C,q)\) using the Principle of Triality for orthogonal transformations. He derives many new expressions for derivations and automorphisms. Also some well-known results are recovered. For example, it is shown as a corollary that all derivations of \(C\) are inner, and \(\dim_F \text{Der}\, C=14\). Furthermore, the Principle of Local Triality in arbitrary characteristic is proved for \(8\)-dimensional composition algebras.
scientific article; zbMATH DE number 1506620
scientific article