Toric-friendly groups

Borovoi, Mikhail; Reichstein, Zinovy

doi:10.2140/ant.2011.5.361

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Toric-friendly groups

Mikhail Borovoi and Zinovy Reichstein

Vol. 5 (2011), No. 3, 361–378

DOI: 10.2140/ant.2011.5.361

Abstract

Let $G$ be a connected linear algebraic group over a field $k$ . We say that $G$ is toric-friendly if for any field extension $K ∕ k$ and any maximal $K$ -torus $T$ in $G$ the group $G (K)$ acts transitively on $(G ∕ T) (K)$ . Our main result is a classification of semisimple (and under certain assumptions on $k$ , of connected) toric-friendly groups.

Keywords

toric-friendly group, linear algebraic group, semisimple group, maximal torus, rational point, elementary obstruction

Mathematical Subject Classification 2000

Primary: 20G10

Secondary: 20G15, 14G05

Milestones

Received: 3 April 2010

Revised: 17 October 2010

Accepted: 17 October 2010

Published: 10 September 2011

Proposed: Jean-Louis Colliot-Th\e'l\e`ne

Seconded: Andrei Zelevinsky, Hendrik W. Lenstra

Authors

Mikhail Borovoi
Tel Aviv University School of Mathematical Sciences 69978 Tel Aviv Israel
http://www.math.tau.ac.il/~borovoi
Zinovy Reichstein
University of British Columbia Department of Mathematics 1984 Mathematics Road Vancouver, BC V6T 1Z2 Canada
http://www.math.ubc.ca/~reichst

Vol. 5, No. 3, 2011