N-determined 2-compact groups. II

Jesper M. Møller. "N-determined 2-compact groups. II." Fundamenta Mathematicae 196.1 (2007): 1-90. <http://eudml.org/doc/283030>.

@article{JesperM2007,
abstract = {This is the second part of a paper about the classification of 2-compact groups. In the first part we set up a general classification procedure and applied it to the simple 2-compact groups of the A-family. In this second part we deal with the other simple Lie groups and with the exotic simple 2-compact group DI(4). We show that all simple 2-compact groups are uniquely N-determined and conclude that all connected 2-compact groups are uniquely N-determined. This means that two connected 2-compact groups are isomorphic if their maximal torus normalizer s are isomorphic and that the automorphisms of a connected 2-compact group are determined by their effect on a maximal torus. As an application we confirm the conjecture that any connected 2-compact group is the product of a compact Lie group with copies of the exceptional 2-compact group DI(4).},
author = {Jesper M. Møller},
journal = {Fundamenta Mathematicae},
keywords = {2-compact groups; uniquely -determined; Quillen category},
language = {eng},
number = {1},
pages = {1-90},
title = {N-determined 2-compact groups. II},
url = {http://eudml.org/doc/283030},
volume = {196},
year = {2007},
}

TY - JOUR
AU - Jesper M. Møller
TI - N-determined 2-compact groups. II
JO - Fundamenta Mathematicae
PY - 2007
VL - 196
IS - 1
SP - 1
EP - 90
AB - This is the second part of a paper about the classification of 2-compact groups. In the first part we set up a general classification procedure and applied it to the simple 2-compact groups of the A-family. In this second part we deal with the other simple Lie groups and with the exotic simple 2-compact group DI(4). We show that all simple 2-compact groups are uniquely N-determined and conclude that all connected 2-compact groups are uniquely N-determined. This means that two connected 2-compact groups are isomorphic if their maximal torus normalizer s are isomorphic and that the automorphisms of a connected 2-compact group are determined by their effect on a maximal torus. As an application we confirm the conjecture that any connected 2-compact group is the product of a compact Lie group with copies of the exceptional 2-compact group DI(4).
LA - eng
KW - 2-compact groups; uniquely -determined; Quillen category
UR - http://eudml.org/doc/283030
ER -