Gradings on the Albert Algebra and on $f_4$

preprint2007arXivOpen access

We study group gradings on the Albert algebra and on the simple exceptional Lie algebra $\frak{f}_4$ 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 $\frak{f}_4$ (also three of them fine).

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Gradings on the Albert Algebra and on $f_4$

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Gradings on the Albert Algebra and on f4f_4f4​

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Gradings on the Albert Algebra and on $f_4$