The classification of p-compact groups for p odd

Summary, in English

A p-compact group, as defined by Dwyer and Wilkerson, is a purely homotopically defined p-local analog of a compact Lie group. It has long been the hope, and later the conjecture, that these objects should have a classification similar to the classification of compact Lie groups. In this paper we finish the proof of this conjecture, for p an odd prime, proving that there is a one-to-one correspondence between connected p-compact groups and finite reflection groups over the p-adic integers. We do this by providing the last, and rather intricate, piece, namely that the exceptional compact Lie groups are uniquely determined as p-compact groups by their Weyl groups seen as finite reflection groups over the p-adic integers. Our approach in fact gives a largely self-contained proof of the entire classification theorem for p odd.

• Author: Kasper Andersen; Jesper Grodal; Jesper Michael Møller; Antonio Viruel
• Publishing year: 2008
• Language: English
• Pages: 95-210
• Publication/Series: Annals of Mathematics
• Volume: 167
• Issue: 1
• Links: http://annals.math.princeton.edu/2008/167-1/p03; http://dx.doi.org/10.4007/annals.2008.167.95
• Document type: Journal article
• Publisher: Annals of Mathematics
• Topic: Mathematics; Computer Vision and Robotics (Autonomous Systems)
• Status: Published
• ISBN/ISSN/Other: ISSN: 0003-486X