On R-triviality of F₄

2019/12/02 by Thakur, Maneesh
#17C30 #20G15 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1912.01433

Abstract

It is known that simple algebraic groups of type F₄ defined over a field k are precisely the full automorphism groups of Albert algebras over k. We explore R-triviality for the group \bf 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 \bf Aut(A) is R-trivial, in the sense of Manin.

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