The Kneser-Tits conjecture for groups with Tits-index E_{8,2}^{66} over an arbitrary field
Group Theory
2010-08-12 v1 K-Theory and Homology
Abstract
We prove: (1) The group of multipliers of similitudes of a 12-dimensional anisotropic quadratic form over a field K with trivial discriminant and split Clifford invariant is generated by norms from quadratic extensions E/K such that q_E is hyperbolic. (2) If G is the group of K-rational points of an absolutely simple algebraic group whose Tits index is E_{8,2}^{66}, then G is generated by its root groups, as predicted by the Kneser-Tits conjecture.
Keywords
Cite
@article{arxiv.1008.1868,
title = {The Kneser-Tits conjecture for groups with Tits-index E_{8,2}^{66} over an arbitrary field},
author = {R. Parimala and J. -P. Tignol and R. M. Weiss},
journal= {arXiv preprint arXiv:1008.1868},
year = {2010}
}