Gradings on the Albert Algebra and on $f_4$

Abstract

We study group gradings on the Albert algebra and on the simple exceptional Lie algebra ${\mathfrak{f}}_4$ over algebraically closed fields of characteristic zero. There are eight nontoral nonequivalent gradings on the Albert algebra (three of them being fine) and nine on ${\mathfrak{f}}_4$ (also three of them fine).

51 pages

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