Vol. 5, No. 3, 2011

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Toric-friendly groups

Mikhail Borovoi and Zinovy Reichstein

Vol. 5 (2011), No. 3, 361–378

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.

toric-friendly group, linear algebraic group, semisimple group, maximal torus, rational point, elementary obstruction
Mathematical Subject Classification 2000
Primary: 20G10
Secondary: 20G15, 14G05
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
Mikhail Borovoi
Tel Aviv University
School of Mathematical Sciences
69978 Tel Aviv
Zinovy Reichstein
University of British Columbia
Department of Mathematics
1984 Mathematics Road
Vancouver, BC V6T 1Z2