Volume 12, issue 3 (2008)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 20
Issue 4, 1807–2438
Issue 3, 1257–1806
Issue 2, 629–1255
Issue 1, 1–627

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Subscriptions
Author Index
To Appear
Contacts
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Automorphisms of $p$–compact groups and their root data

Kasper K S Andersen and Jesper Grodal

Geometry & Topology 12 (2008) 1427–1460
Abstract

We construct a model for the space of automorphisms of a connected p–compact group in terms of the space of automorphisms of its maximal torus normalizer and its root datum. As a consequence we show that any homomorphism to the outer automorphism group of a p–compact group can be lifted to a group action, analogous to a classical theorem of de Siebenthal for compact Lie groups. The model of this paper is used in a crucial way in our paper ‘The classification of 2-compact groups’ [arXiv:math.AT/0611437], where we prove the conjectured classification of 2–compact groups and determine their automorphism spaces.

Keywords
$p$-compact group, root datum, maximal torus normalizer
Mathematical Subject Classification 2000
Primary: 55R35
Secondary: 20G99, 22E15, 55P35
References
Publication
Received: 11 January 2007
Revised: 1 April 2008
Accepted: 30 November 2007
Published: 10 June 2008
Proposed: Haynes Miller
Seconded: Paul Goerss, Ralph Cohen
Authors
Kasper K S Andersen
Department of Mathematical Sciences
University of Aarhus
DK-8000 Aarhus C
Denmark
http://person.au.dk/en/kksa@imf.au.dk
Jesper Grodal
Department of Mathematical Sciences
University of Copenhagen
DK-2100 Copenhagen
Denmark
http://www.math.ku.dk/~jg