Fine gradings on Kantor systems of Hurwitz type.

Abstract

In this article fine group gradings by abelian groups on Kantor pairs and Kantor triple systems associated with Hurwitz algebras (unital composition algebras) are studied. These gradings are classified up to equivalence over an algebraically closed field of characteristic different from 2. Moreover, the corresponding universal grading groups and Weyl groups are computed and the gradings induced on related Lie algebras obtained through the Kantor construction are analized, providing a detailed structural description of these algebraic systems.