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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:
author
publishing date
type
Contribution to journal
publication status
published
subject
in
Annals of Mathematics
volume
167
issue
1
pages
95 - 210
publisher
Annals of Mathematics
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
2013-04-25 16:27:35
date last changed
2017-08-06 03:50:33
@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    = {Annals of Mathematics},
  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},
  volume       = {167},
  year         = {2008},
}