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

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...

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Published inForum of mathematics. Sigma Vol. 9
Main Authors Alsaody, Seidon, Chernousov, Vladimir, Pianzola, Arturo
Format Journal Article
LanguageEnglish
Published 2021
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Summary: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 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 $^1\mathrm {E}_6$ .
ISSN:2050-5094
2050-5094
DOI:10.1017/fms.2021.65