Geometry & Topology

Automorphisms of $p$–compact groups and their root data

Kasper K S Andersen and Jesper Grodal

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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.

Article information

Source
Geom. Topol., Volume 12, Number 3 (2008), 1427-1460.

Dates
Received: 11 January 2007
Revised: 1 April 2008
Accepted: 30 November 2007
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513800101

Digital Object Identifier
doi:10.2140/gt.2008.12.1427

Mathematical Reviews number (MathSciNet)
MR2421132

Zentralblatt MATH identifier
1152.55006

Subjects
Primary: 55R35: Classifying spaces of groups and $H$-spaces
Secondary: 20G99: None of the above, but in this section 22E15: General properties and structure of real Lie groups 55P35: Loop spaces

Keywords
$p$-compact group root datum maximal torus normalizer

Citation

Andersen, Kasper K S; Grodal, Jesper. Automorphisms of $p$–compact groups and their root data. Geom. Topol. 12 (2008), no. 3, 1427--1460. doi:10.2140/gt.2008.12.1427. https://projecteuclid.org/euclid.gt/1513800101


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