Vol. 279, No. 1-2, 2015

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On maximal tori of algebraic groups of type $G_2$

Constantin Beli, Philippe Gille and Ting-Yu Lee

Vol. 279 (2015), No. 1-2, 101–134
Abstract

Given an octonion algebra C over a field k, its automorphism group is an algebraic semisimple k-group of type G2. We study the maximal tori of G in terms of the algebra C.

To the memory of Robert Steinberg

Keywords
Octonions, tori, Galois cohomology, homogeneous spaces
Mathematical Subject Classification 2010
Primary: 20G15, 17A75
Secondary: 11E57, 20G41
Milestones
Received: 9 November 2014
Revised: 29 January 2015
Accepted: 2 February 2015
Published: 21 December 2015
Authors
Constantin Beli
Institute of Mathematics Simion Stoilow of the Romanian Academy
Calea Grivitei 21,
RO-010702 Bucharest
Romania
Philippe Gille
Université Claude Bernard Lyon 1
UMR 5208 du CNRS
Institut Camille Jordan
43 boulevard du 11 novembre 1918
69622 Villeurbanne
France
Ting-Yu Lee
Ecole Polytechnique Fédérale de Lausanne
EPFL Station 8
CH-1015 Lausanne
Switzerland