Some Graded Identities of The Cayley-Dickson Algebra

Abstract

We work to find a basis of graded identities for the octonion algebra. We do so for the ${\mathbb{Z}}_2^2$ and ${\mathbb{Z}}_2^3$ gradings, both of them derived of the Cayley-Dickson process, the later grading being possible only when the characteristic of the scalars is not two.