Gradings on the exceptional Lie algebras $F_4$ and $G_2$ revisited
Alberto Elduque (Universidad de Zaragoza), Mikhail Kochetov, (Memorial University of Newfoundland)
TL;DR
This paper classifies all abelian group gradings on certain exceptional Lie algebras and related structures over algebraically closed fields, providing a comprehensive understanding of their grading structures.
Contribution
It offers a complete classification of abelian group gradings on the simple Lie algebras of types G2 and F4, and on the exceptional Jordan algebra, over algebraically closed fields.
Findings
Classified all abelian group gradings on G2 and F4 Lie algebras
Classified gradings on the exceptional simple Jordan algebra
Results hold over algebraically closed fields of characteristic not 2 (and not 3 for G2)
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 (characteristic not 3), the exceptional simple Jordan algebra, and the simple Lie algebra of type .
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