Revista Matemática Iberoamericana

Gradings on the Albert algebra and on $\mathfrak{f}_4$

Cristina Draper and Cándido Martín
Source: Rev. Mat. Iberoamericana Volume 25, Number 3 (2009), 841-908.

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).

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Primary Subjects: 17B25
Secondary Subjects: 17C40
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Permanent link to this document: http://projecteuclid.org/euclid.rmi/1257258097
Zentralblatt MATH identifier: 05663366
Mathematical Reviews number (MathSciNet): MR2590049

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