N-determined 2-compact groups. I

Jesper M. Møller

Fundamenta Mathematicae (2007)

  • Volume: 195, Issue: 1, page 11-84
  • ISSN: 0016-2736

Abstract

top
This is the first part of a paper that classifies 2-compact groups. In this first part we formulate a general classification scheme for 2-compact groups in terms of their maximal torus normalizer pairs. We apply this general classification procedure to the simple 2-compact groups of the A-family and show that any simple 2-compact group that is locally isomorphic to PGL(n+1,ℂ) is uniquely N-determined. Thus there are no other 2-compact groups in the A-family than the ones we already know. We also compute the group of automorphisms of any member of the A-family and show that it consists of unstable Adams operations only.

How to cite

top

Jesper M. Møller. "N-determined 2-compact groups. I." Fundamenta Mathematicae 195.1 (2007): 11-84. <http://eudml.org/doc/282940>.

@article{JesperM2007,
abstract = {This is the first part of a paper that classifies 2-compact groups. In this first part we formulate a general classification scheme for 2-compact groups in terms of their maximal torus normalizer pairs. We apply this general classification procedure to the simple 2-compact groups of the A-family and show that any simple 2-compact group that is locally isomorphic to PGL(n+1,ℂ) is uniquely N-determined. Thus there are no other 2-compact groups in the A-family than the ones we already know. We also compute the group of automorphisms of any member of the A-family and show that it consists of unstable Adams operations only.},
author = {Jesper M. Møller},
journal = {Fundamenta Mathematicae},
keywords = {2-compact groups; uniquely -determined; Quillen category},
language = {eng},
number = {1},
pages = {11-84},
title = {N-determined 2-compact groups. I},
url = {http://eudml.org/doc/282940},
volume = {195},
year = {2007},
}

TY - JOUR
AU - Jesper M. Møller
TI - N-determined 2-compact groups. I
JO - Fundamenta Mathematicae
PY - 2007
VL - 195
IS - 1
SP - 11
EP - 84
AB - This is the first part of a paper that classifies 2-compact groups. In this first part we formulate a general classification scheme for 2-compact groups in terms of their maximal torus normalizer pairs. We apply this general classification procedure to the simple 2-compact groups of the A-family and show that any simple 2-compact group that is locally isomorphic to PGL(n+1,ℂ) is uniquely N-determined. Thus there are no other 2-compact groups in the A-family than the ones we already know. We also compute the group of automorphisms of any member of the A-family and show that it consists of unstable Adams operations only.
LA - eng
KW - 2-compact groups; uniquely -determined; Quillen category
UR - http://eudml.org/doc/282940
ER -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.