On the Tits-Weiss Conjecture and the Kneser-Tits Conjecture for $\mathrm{E}^{78}_{7,1}$ and $\mathrm{E}^{78}_{8,2}$
Rings and Algebras
2019-12-02 v1 Algebraic Geometry
Group Theory
Abstract
We prove that the structure group of any Albert algebra over an arbitrary field is -trivial. This implies the Tits-Weiss conjecture for Albert algebras and the Kneser-Tits conjecture for isotropic groups of type . As a further corollary, we show that some standard conjectures on the groups of -equivalence classes in algebraic groups and the norm principle are true for strongly inner forms of type .
Keywords
Cite
@article{arxiv.1911.12908,
title = {On the Tits-Weiss Conjecture and the Kneser-Tits Conjecture for $\mathrm{E}^{78}_{7,1}$ and $\mathrm{E}^{78}_{8,2}$},
author = {Seidon Alsaody and Vladimir Chernousov and Arturo Pianzola},
journal= {arXiv preprint arXiv:1911.12908},
year = {2019}
}
Comments
With an Appendix by Richard M.\ Weiss