Gradings on the exceptional Lie algebras $F_4$ and $G_2$ revisited

Abstract

All gradings by abelian groups are classified on the following algebras over an algebraically closed field of characteristic not 2: the simple Lie algebra of type $G_2$ (characteristic not 3), the exceptional simple Jordan algebra, and the simple Lie algebra of type $F_4$.

arXiv comment36 pages. References expanded and updated