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European Mathematical Society Publishing House
2016-09-19 17:05:45
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
25
2009
3
Gradings on the Albert algebra and on $\mathfrak{f}_4$
Cristina
Draper Fontanals
Universidad de Málaga, MÁLAGA, SPAIN
Cándido
Martín González
Universidad de Málaga, MÁLAGA, SPAIN
Exceptional Lie algebra, grading, algebraic group, Weyl group
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).
Nonassociative rings and algebras
General
841
908
10.4171/RMI/585
http://www.ems-ph.org/doi/10.4171/RMI/585