2019
DOI: 10.48550/arxiv.1912.01433
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On $R$-triviality of $F_4$

Maneesh Thakur

Abstract: It is known that simple algebraic groups of type F 4 defined over a field k are precisely the full automorphism groups of Albert algebras over k. We explore R-triviality for the group Aut(A) when A is an Albert algebra. In this paper, we consider the case when A is an Albert division algebra, that arises from the first Tits construction. We prove that Aut(A) is R-trivial, in the sense of Manin.

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