A canonical form for automorphisms of totally disconnected locally compact groups. (English) Zbl 1057.22005
Kaimanovich, Vadim A. (ed.), Random walks and geometry. Proceedings of a workshop at the Erwin Schrödinger Institute, Vienna, June 18 – July 13, 2001. In collaboration with Klaus Schmidt and Wolfgang Woess. Collected papers. Berlin: de Gruyter (ISBN 3-11-017237-2/hbk). 295-316 (2004).
A canonical form for the automorphisms of totally disconnected locally compact groups (1994, 2001, 2004, Willis), described in terms of the action of the automorphism on certain compact open groups, known as tidy subgroups, is considered. It is pointed out that the problem of identifying tidy subgroups is analogous to finding a basis which triangularises a linear transformation. Similarly, a canonical form for the automorphisms of general totally disconnected groups provides analogues of the eigenspaces and eigenvalues of the automorphism of the Lie algebra of a Lie group. In the paper under review some examples of totally disconnected groups are listed. An algorithm for finding tidy subgroups (tidying procedure) is described. A dynamical description of tidy subgroups is also given. In conclusion, some applications of the approach under consideration are briefly discussed.
For the entire collection see [Zbl 1047.60001].
For the entire collection see [Zbl 1047.60001].
Reviewer: A. A. Bogush (Minsk)
MSC:
| 22D05 | General properties and structure of locally compact groups |
| 22D45 | Automorphism groups of locally compact groups |
| 20E36 | Automorphisms of infinite groups |
| 20F28 | Automorphism groups of groups |
| 20D45 | Automorphisms of abstract finite groups |
