On the Tits–Weiss conjecture and the Kneser–Tits conjecture for and (With an Appendix by R. M. Weiss)
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Published:2021
Issue:
Volume:9
Page:
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ISSN:2050-5094
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Container-title:Forum of Mathematics, Sigma
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language:en
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Short-container-title:Forum of Mathematics, Sigma
Author:
Alsaody Seidon,Chernousov Vladimir,Pianzola Arturo
Abstract
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
$^1\mathrm {E}_6$
.
Publisher
Cambridge University Press (CUP)
Subject
Computational Mathematics,Discrete Mathematics and Combinatorics,Geometry and Topology,Mathematical Physics,Statistics and Probability,Algebra and Number Theory,Theoretical Computer Science,Analysis
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