JournalsrmiVol. 25, No. 3pp. 841–908

Gradings on the Albert algebra and on f4\mathfrak{f}_4

  • Cándido Martín González

    Universidad de Málaga, Spain
  • Cristina Draper Fontanals

    Universidad de Málaga, Spain
Gradings on the Albert algebra and on $\mathfrak{f}_4$ cover
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Abstract

We study group gradings on the Albert algebra and on the exceptional simple Lie algebra f4\frak{f}_4 over algebraically closed fields of characteristic zero. The immediate precedent of this work is [Draper, C. and Martin, C.: Gradings on g2\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 g2\frak{g}_2. In the cases of the Albert algebra and f4\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 f4\frak{f}_4 (also three of them fine).

Cite this article

Cándido Martín González, Cristina Draper Fontanals, Gradings on the Albert algebra and on f4\mathfrak{f}_4. Rev. Mat. Iberoam. 25 (2009), no. 3, pp. 841–908

DOI 10.4171/RMI/585