Z n -Orthograded Monocomposition Algebras

We study NQM algebras A having an orthogonal automorphism of finite order n 3 (called Z _n -orthograded NQM algebras). The Z ₃-orthograded NQM algebras of dimension 7 are treated in more detail. In particular, we find all algebras A which are not bi-isotropic in this class, and for every algebra A, determine an automorphism group Aut,A and an orthogonal automorphism group Ortaut,A. In constructing and classifying (up to isomorphism) NQM algebras, use is made of orthogonal decompositions of the algebras.