Automorphism group schemes of Kantor pairs of associative central simple structurable algebras

Abstract

In this work, a description of the automorphism group schemes is given for the Kantor pairs (and for some Kantor triple systems related to them) associated to associative central simple structurable algebras in the three ``split'' cases, where the base field is algebraically closed of characteristic different from $2$. For two of the three cases (the ones with orthogonal and symplectic involutions), we relate the decomposition (as a central product) of the automorphism group scheme to a decomposition (as a tensor product) of the corresponding Kantor pair regarded as a metric generalized Jordan pair.