Gradings on the exceptional Lie algebras \(F_4\) and \(G_2\) revisited
type: Item
instance of: scholarly article
title: Gradings on the exceptional Lie algebras \(F_4\) and \(G_2\) revisited
zbMATH Open document ID: 1303.17019
DOI: 10.4171/RMI/691
author: Alberto Elduque
author: Mikhail Kochetov
published in: Revista Matemática Iberoamericana
publication date: 2012-09-06T00:00:00Z
full work available at URL: https://arxiv.org/abs/1009.1218
review text: The authors describe all gradings on central simple Lie algebras of type \(G_2\) over an arbitrary field of characteristic other than \(2\) and \(3\) and classify the gradings up to equivalence and up to isomorphism, assuming the field to be algebraically closed. They also give constructions of four fine gradings in the Albert algebra over an algebraically closed field of characteristic different from \(2\) (as pointed out by the authors, one of them is not present in characteristic \(3\)). Then, they prove that these gradings exhaust the list of fine gradings up to equivalence. Finally they classify all gradings on the simple Lie algebra of type \(F_4\) under the same assumptions on the ground field. Since the authors work over field of prime characteristic, the techniques used involve algebraic groups (in the sense of affine group schemes). The relation of properties related to gradings with the automorphism group schemes is explained in section 2 of the paper.
Mathematics Subject Classification ID: 17B70
Mathematics Subject Classification ID: 17B25
zbMATH DE Number: 6078123
zbMATH Keywords: graded algebra
zbMATH Keywords: fine grading
zbMATH Keywords: Weyl group
zbMATH Keywords: octonions
zbMATH Keywords: Albert algebra
zbMATH Keywords: G2
zbMATH Keywords: F4
reviewed by: Candido Martín González
MaRDI profile type: Publication
arXiv ID: 1009.1218
cites work: Classification of group gradings on simple Lie algebras of types \(\mathcal A\), \(\mathcal B\), \(\mathcal C\) and \(\mathcal D\)
cites work: Group gradings on simple Lie algebras in positive characteristic
cites work: Group gradings on associative algebras
description: scientific article; zbMATH DE number 6078123