$N$-determined 2-compact groups. I

Jesper M. Møller¹

¹ Matematisk Institut Universitetsparken 5 DK-2100 København, Denmark

Fundamenta Mathematicae, Tome 195 (2007) no. 1, pp. 11-84.

Résumé

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 $\mathrm{A}$-family and show that any simple $2$-compact group that is locally isomorphic to ${\rm PGL}(n+1,{\mathbb C})$ is uniquely $N$-determined. Thus there are no other $2$-compact groups in the $\mathrm{A}$-family than the ones we already know. We also compute the group of automorphisms of any member of the $\mathrm{A}$-family and show that it consists of unstable Adams operations only.

Détail

DOI : 10.4064/fm195-1-2

Keywords: first part paper classifies compact groups first part formulate general classification scheme compact groups terms their maximal torus normalizer pairs apply general classification procedure simple compact groups mathrm family simple compact group locally isomorphic pgl mathbb uniquely n determined there other compact groups mathrm family already know compute group automorphisms member mathrm family consists unstable adams operations only