We study group gradings on the Albert algebra and on the exceptional simple Lie algebra over algebraically closed fields of characteristic zero. The immediate precedent of this work is [Draper, C. and Martin, C.: Gradings on . Linear Algebra Appl. 418 (2006), no. 1, 85-111] where we described (up to equivalence) all the gradings on the exceptional simple Lie algebra . In the cases of the Albert algebra and , 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 (also three of them fine).
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Cándido Martín González, Cristina Draper Fontanals, Gradings on the Albert algebra and on . Rev. Mat. Iberoam. 25 (2009), no. 3, pp. 841–908