Automorphisms of p–compact groups and their root data

Andersen, Kasper K S¹ ; Grodal, Jesper²

¹ Department of Mathematical Sciences, University of Aarhus, DK-8000 Aarhus C, Denmark
² Department of Mathematical Sciences, University of Copenhagen, DK-2100 Copenhagen, Denmark

Geometry & topology, Tome 12 (2008) no. 3, pp. 1427-1460.

Résumé

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.

Détail

DOI : 10.2140/gt.2008.12.1427

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

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