Gradings on the Albert algebra and on $\mathfrak{f}_4$
Rev. Mat. Iberoamericana, Tome 25 (2009) no. 1, p. 841-908 / Harvested from Project Euclid
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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).
Publié le : 2009-06-15
Classification:  exceptional Lie algebra,  grading,  algebraic group,  Weyl group,  17B25,  17C40 
@article{1257258097,
     author = {Draper
, 
Cristina and Mart\'\i n
, 
C\'andido},
     title = {Gradings on the Albert algebra and on $\mathfrak{f}\_4$},
     journal = {Rev. Mat. Iberoamericana},
     volume = {25},
     number = {1},
     year = {2009},
     pages = { 841-908},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1257258097}
}

Draper
, 
Cristina; Martín
, 
Cándido. Gradings on the Albert algebra and on $\mathfrak{f}_4$. Rev. Mat. Iberoamericana, Tome 25 (2009) no. 1, pp.  841-908. http://gdmltest.u-ga.fr/item/1257258097/