Weyl images of Kantor pairs

Abstract

Kantor pairs arise naturally in the study of 5-graded Lie algebras. In this article, we begin the study of simple Kantor pairs of arbitrary dimension. We introduce Weyl images of Kantor pairs and use them to construct examples of Kantor pairs including a new class of central simple Kantor pairs.Comment: 43 pages. In the last section of this new version, the assumption that the ring of scalars is a field is dropped. This allows the construction of many forms of split Kantor pairs of type $E_6$ over rings. To facilitate this change, some small revisions are made in earlier sections. To be published in the Canadian Journal of Mathematic