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2008 Automorphisms of $p$–compact groups and their root data
Kasper K S Andersen, Jesper Grodal
Geom. Topol. 12(3): 1427-1460 (2008). DOI: 10.2140/gt.2008.12.1427

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.

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Kasper K S Andersen. Jesper Grodal. "Automorphisms of $p$–compact groups and their root data." Geom. Topol. 12 (3) 1427 - 1460, 2008. https://doi.org/10.2140/gt.2008.12.1427

Information

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

zbMATH: 1152.55006
MathSciNet: MR2421132
Digital Object Identifier: 10.2140/gt.2008.12.1427

Subjects:
Primary: 55R35
Secondary: 20G99 , 22E15 , 55P35

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

Rights: Copyright © 2008 Mathematical Sciences Publishers

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