$N$-determined 2-compact groups. II

Jesper M. Møller¹

¹ Matematisk Institut Universitetsparken 5 DK-2100 København, Denmark

Fundamenta Mathematicae, Tome 196 (2007) no. 1, pp. 1-90

Résumé

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 $\rm A$-family. In this second part we deal with the other simple Lie groups and with the exotic simple $2$-compact group ${\rm DI}(4)$. 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 ${\rm DI}(4)$.

Détail

DOI : 10.4064/fm196-1-1

Keywords: second part paper about classification compact groups first part set general classification procedure applied simple compact groups a family second part other simple lie groups exotic simple compact group simple compact groups uniquely n determined conclude connected compact groups uniquely n determined means connected compact groups isomorphic their maximal torus normalizer isomorphic automorphisms connected compact group determined their effect maximal torus application confirm conjecture connected compact group product compact lie group copies exceptional compact group