The classification of pcompact groups for p odd
(2008) In Annals of Mathematics 167(1). p.95210 Abstract
 A pcompact group, as defined by Dwyer and Wilkerson, is a purely homotopically defined plocal 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 onetoone correspondence between connected pcompact groups and finite reflection groups over the padic integers. We do this by providing the last, and rather intricate, piece, namely that the exceptional compact Lie groups are uniquely determined as pcompact groups by their Weyl groups seen as finite reflection groups over the padic integers. Our approach in fact... (More)
 A pcompact group, as defined by Dwyer and Wilkerson, is a purely homotopically defined plocal 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 onetoone correspondence between connected pcompact groups and finite reflection groups over the padic integers. We do this by providing the last, and rather intricate, piece, namely that the exceptional compact Lie groups are uniquely determined as pcompact groups by their Weyl groups seen as finite reflection groups over the padic integers. Our approach in fact gives a largely selfcontained proof of the entire classification theorem for p odd. (Less)
Please use this url to cite or link to this publication:
http://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
 Annals of Mathematics
 external identifiers

 scopus:42149172678
 ISSN
 0003486X
 DOI
 10.4007/annals.2008.167.95
 language
 English
 LU publication?
 no
 id
 80ccfa1248c7490b9c741eefd39be652 (old id 3412535)
 alternative location
 http://annals.math.princeton.edu/2008/1671/p03
 date added to LUP
 20130425 16:27:35
 date last changed
 20170806 03:50:33
@article{80ccfa1248c7490b9c741eefd39be652, abstract = {A pcompact group, as defined by Dwyer and Wilkerson, is a purely homotopically defined plocal 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 onetoone correspondence between connected pcompact groups and finite reflection groups over the padic integers. We do this by providing the last, and rather intricate, piece, namely that the exceptional compact Lie groups are uniquely determined as pcompact groups by their Weyl groups seen as finite reflection groups over the padic integers. Our approach in fact gives a largely selfcontained proof of the entire classification theorem for p odd.}, author = {Andersen, Kasper and Grodal, Jesper and Møller, Jesper Michael and Viruel, Antonio}, issn = {0003486X}, language = {eng}, number = {1}, pages = {95210}, publisher = {Annals of Mathematics}, series = {Annals of Mathematics}, title = {The classification of pcompact groups for p odd}, url = {http://dx.doi.org/10.4007/annals.2008.167.95}, volume = {167}, year = {2008}, }