Automorphisms of p-compact groups and their root data

Details Automorphisms of p-compact groups and their root data Automorphisms of p-compact groups and their root data

2005-10-10

arxiv.org/abs/math/0510179v2

Geometry & Topology 12 (2008) 1427-1460

Mathematics

Algebraic Topology

24 pages. Introduction restructured and title changed (from "Automorphisms of root data, maximal torus normalizers, and p-comp

Scientific paper

10.2140/gt.2008.12.1427

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'', where we prove the conjectured classification of 2-compact groups and determine their automorphism spaces.

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