The classification of p-compact groups for p odd
Andersen, Kasper LU
; Grodal, Jesper
; Møller, Jesper Michael
and Viruel, Antonio
(2008)
In Annals of Mathematics
167(1).
p.95-210
- Abstract
- 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... (More)
- 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. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/3412535
- author
- Andersen, Kasper
LU
; Grodal, Jesper
; Møller, Jesper Michael
and Viruel, Antonio
- publishing date
- 2008
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Annals of Mathematics
- volume
- 167
- issue
- 1
- pages
- 95 - 210
- publisher
- Department of Mathematics at Princeton University
- external identifiers
-
- scopus:42149172678
- ISSN
- 0003-486X
- DOI
- 10.4007/annals.2008.167.95
- language
- English
- LU publication?
- no
- id
- 80ccfa12-48c7-490b-9c74-1eefd39be652 (old id 3412535)
- alternative location
- http://annals.math.princeton.edu/2008/167-1/p03
- date added to LUP
- 2016-04-01 12:33:40
- date last changed
- 2025-10-14 12:38:19
@article{80ccfa12-48c7-490b-9c74-1eefd39be652,
abstract = {{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 = {{Andersen, Kasper and Grodal, Jesper and Møller, Jesper Michael and Viruel, Antonio}},
issn = {{0003-486X}},
language = {{eng}},
number = {{1}},
pages = {{95--210}},
publisher = {{Department of Mathematics at Princeton University}},
series = {{Annals of Mathematics}},
title = {{The classification of p-compact groups for p odd}},
url = {{http://dx.doi.org/10.4007/annals.2008.167.95}},
doi = {{10.4007/annals.2008.167.95}},
volume = {{167}},
year = {{2008}},
}