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arXiv · 1911.12910

$R$-triviality of Groups of Type ${\rm F}_4$ Arising from the First Tits Construction

Seidon Alsaody·Vladimir Chernousov·Arturo Pianzola
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Abstract

Any group of type ${\rm F}_4$ is obtained as the automorphism group of an Albert algebra. We prove that such a group is $R$-trivial whenever the Albert algebra is obtained from the first Tits construction. Our proof uses cohomological techniques and the corresponding result on the structure group of such Albert algebras.

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Seidon Alsaody, Vladimir Chernousov, Arturo Pianzola. 2019-11-29. $R$-triviality of Groups of Type ${\rm F}_4$ Arising from the First Tits Construction. https://doi.org/10.1112/blms.12440

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