On the Tits-Weiss Conjecture and the Kneser-Tits Conjecture for E⁷⁸_7,1 and E⁷⁸_8,2

2019/11/29 by Seidon Alsaody, Alsaody, Seidon, Vladimir Chernousov +3
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1911.12908

openalex publication_date 2019/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the structure group of any Albert algebra over an arbitrary field is R-trivial. This implies the Tits-Weiss conjecture for Albert algebras and the Kneser-Tits conjecture for isotropic groups of type E_7,1⁷⁸, E_8,2⁷⁸. As a further corollary, we show that some standard conjectures on the groups of R-equivalence classes in algebraic groups and the norm principle are true for strongly inner forms of type ¹E₆.

Related

• Albert algebras and the Tits-Weiss conjecture
• Automorphisms of Albert algebras and a conjecture of Tits and Weiss
• R-triviality of some exceptional groups
• The Kneser-Tits conjecture for groups with Tits-index E_8,2⁶⁶ over an arbitrary field
• On R-triviality of F₄