Gradings on the Albert Algebra and on $f_4$

Mathematics – Rings and Algebras

Scientific paper

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51 pages

Scientific paper

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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