On the Tits–Weiss conjecture and the Kneser–Tits conjecture for and (With an Appendix by R. M. Weiss)

• Published in: Forum of mathematics. Sigma Vol. 9
• Main Authors: Alsaody, Seidon, Chernousov, Vladimir, Pianzola, Arturo
• Format: Journal Article
• Language: English
• Published: 2021

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 $\mathrm {E}_{7,1}^{78}, \mathrm {E}_{8,2}^{78}$ . As a further corollary, we...