Revista Matemática Iberoamericana


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Volume 28, Issue 3, 2012, pp. 773–813
DOI: 10.4171/RMI/691

Published online: 2012-07-16

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

Alberto Elduque[1] and Mikhail Kochetov[2]

(1) Universidad de Zaragoza, Spain
(2) Memorial University of Newfoundland, St. John's, Canada

All gradings by abelian groups are classified on the following algebras over an algebraically closed field $\mathbb{F}$: the simple Lie algebra of type $G_2$ (char $\mathbb{F}\ne 2,3$), the exceptional simple Jordan algebra (char $\mathbb{F}\ne 2$), and the simple Lie algebra of type $F_4$ (char $\mathbb{F} \ne 2$).

Keywords: Graded algebra, fine grading, Weyl group, octonions, Albert algebra

Elduque Alberto, Kochetov Mikhail: Gradings on the exceptional Lie algebras $F_4$ and $G_2$ revisited. Rev. Mat. Iberoamericana 28 (2012), 773-813. doi: 10.4171/RMI/691