Vol. 5, No. 3, 2011

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Toric-friendly groups

Mikhail Borovoi and Zinovy Reichstein

Vol. 5 (2011), No. 3, 361–378
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 Kk and any maximal K-torus T in G the group G(K) acts transitively on (GT)(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