Fine gradings on Kantor systems of Hurwitz type

TL;DR

This paper classifies fine abelian group gradings on Kantor pairs and triple systems related to Hurwitz algebras, computes their universal and Weyl groups, and explores induced gradings on associated Lie algebras.

Contribution

It provides a comprehensive classification of fine gradings on Kantor systems of Hurwitz type, including universal and Weyl groups, and analyzes induced gradings on related Lie algebras.

Findings

Classification of fine gradings on Kantor pairs and triples

Computation of universal and Weyl groups for these gradings

Determination of induced gradings on associated Lie algebras

Abstract

We give a classification up to equivalence of the fine group gradings by abelian groups on the Kantor pairs and triple systems associated to 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.