Fine gradings on Kantor systems of Hurwitz type

Abstract

We give a classification up to equivalence of the fine group gradings by abelian groups on the Kantor pairs and triple systems associated with Hurwitz algebras (i.e., unital composition algebras), under the assumption that the base field is algebraically closed of characteristic different from 2. The universal groups and associated Weyl groups are computed. We also determine, in the case of Kantor pairs, the induced (fine) gradings on the associated Lie algebras given by the Kantor construction.