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October, 2009 Gradings on the Albert algebra and on $\mathfrak{f}_4$
Cristina Draper , Cándido Martín
Rev. Mat. Iberoamericana 25(3): 841-908 (October, 2009).

Abstract

We study group gradings on the Albert algebra and on the exceptional simple Lie algebra $\frak{f}_4$ over algebraically closed fields of characteristic zero. The immediate precedent of this work is [Draper, C. and Martin, C.: Gradings on $\frak{g}_2$. Linear Algebra Appl. 418 (2006), no. 1, 85-111] where we described (up to equivalence) all the gradings on the exceptional simple Lie algebra $\frak{g}_2$. In the cases of the Albert algebra and $\frak{f}_4$, we look for the nontoral gradings finding that there are only eight nontoral nonequivalent gradings on the Albert algebra (three of them being fine) and nine on $\frak{f}_4$ (also three of them fine).

Citation

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Cristina Draper . Cándido Martín . "Gradings on the Albert algebra and on $\mathfrak{f}_4$." Rev. Mat. Iberoamericana 25 (3) 841 - 908, October, 2009.

Information

Published: October, 2009
First available in Project Euclid: 3 November 2009

zbMATH: 1281.17035
MathSciNet: MR2590049

Subjects:
Primary: 17B25
Secondary: 17C40

Rights: Copyright © 2009 Departamento de Matemáticas, Universidad Autónoma de Madrid

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Vol.25 • No. 3 • October, 2009
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