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Automorphisms of
$p$–compact groups and their root data
Kasper K S Andersen and Jesper Grodal |
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Geometry & Topology 12 (2008) 1427–1460
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Abstract |
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We construct a model for the space of automorphisms of a connected –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 –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 –compact groups and determine their automorphism spaces. |
Keywords
$p$-compact group, root datum, maximal torus normalizer
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Mathematical Subject Classification 2000
Primary: 55R35
Secondary: 20G99, 22E15, 55P35
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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
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Authors |
| Kasper K S Andersen | |
| Department of Mathematical
Sciences University of Aarhus DK-8000 Aarhus C Denmark |
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| http://person.au.dk/en/kksa@imf.au.dk | |
| Jesper Grodal | |
| Department of Mathematical
Sciences University of Copenhagen DK-2100 Copenhagen Denmark |
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| http://www.math.ku.dk/~jg | |
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