Gradings on tensor products of composition algebras and on the Smirnov algebra.

Abstract

In this article group gradings on tensor products of composition algebras are studied, particularly those involving a Cayley algebra and a Hurwitz algebra, over fields of characteristic different from 2. These gradings are classified up to equivalence and isomorphism and the corresponding automorphism group schemes are analyzed. It is also shown that the automorphism group of the Smirnov algebra, a 35-dimensional exceptional structurable algebra built from a Cayley algebra, is closely related to that of the Cayley algebra, allowing a classification of its group gradings.