Automorphisms of p-compact groups and their root data
Author
Summary, in English
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 [2], where we prove the conjectured classification of 2–compact groups and determine their automorphism spaces.
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 [2], where we prove the conjectured classification of 2–compact groups and determine their automorphism spaces.
Publishing year
2008
Language
English
Pages
1427-1460
Publication/Series
Geometry and Topology
Volume
12
Issue
3
Document type
Journal article
Publisher
Mathematical Sciences Publishers
Topic
- Mathematics
Status
Published
ISBN/ISSN/Other
- ISSN: 1364-0380