5-Graded simple Lie algebras, structurable algebras, and Kantor pairs

Abstract

Relying on the classification of simple Lie algebras over algebraically closed fields of characteristic >3, we show that any finite-dimensional central simple 5-graded Lie algebra over a field k of characteristic ≠2,3 is a simple Lie algebra of Chevalley type, i.e. a central quotient of the Lie algebra of a simple algebraic k-group. As a consequence, we prove that all central simple structurable algebras and Kantor pairs over k arise from 5-gradings on simple Lie algebras of Chevalley type.