Abstract simplicity of locally compact Kac-Moody groups

Abstract

In this paper, we establish that complete Kac-Moody groups over finite fields are abstractly simple. The proof makes an essential use of Mathieu-Rousseau's construction of complete Kac-Moody groups over fields. This construction has the advantage that both real and imaginary root spaces of the Lie algebra lift to root subgroups over arbitrary fields. A key point in our proof is the fact, of independent interest, that both real and imaginary root subgroups are contracted by conjugation of positive powers of suitable Weyl group elements.

17 pages; the appendix by Caprace-Reid-Willis has been removed as it is now part of http://arxiv.org/abs/1304.6246. The proof of Theorems A and B has been simplified, and a Corollary F has been added

References in corpus (1)

• The Nub of an Automorphism of a Totally Disconnected, Locally Compact Group

Cited by in corpus (3)

• Locally normal subgroups of totally disconnected groups. Part II: Compactly generated simple groups
• Totally disconnected locally compact groups with a linear open subgroup
• Approximating simple locally compact groups by their dense locally compact subgroups