Automorphisms of p–compact groups and their root data
KKS Andersen, J Grodal - Geometry & Topology, 2008 - msp.org
KKS Andersen, J Grodal
Geometry & Topology, 2008•msp.orgWe 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 ap–
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 …
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 ap–
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 …
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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