- Title
- Tidy subgroups for commuting automorphisms of totally disconnected groups: an analogue of simultaneous triangularisation of matrices
- Creator
- Willis, George A.
- Relation
- New York Journal of Mathematics Vol. 10, p. 1-35
- Relation
- http://8000-nyjm.albany.edu.library.newcastle.edu.au/j/2004/10-1.html
- Publisher
- Electronic Journals Project
- Resource Type
- journal article
- Date
- 2004
- Description
- Let α be an automorphism of the totally disconnected group G. The compact open subgroup, V, of G is tidy for α if [α(V') : α(V')∩ V'] is minimised at V, where V' ranges over all compact open subgroups of G. Identifying a subgroup tidy for α is analogous to identifying a basis which puts a linear transformation into Jordan canonical form. This analogy is developed here by showing that commuting automorphisms have a common tidy subgroup of G and, conversely, that a group siH of automorphisms having a common tidy subgroup V is abelian modulo the automorphisms which leave V invariant. Certain subgroups of G are the analogues of eigenspaces and corresponding real characters of siH the analogues of eigenvalues.
- Subject
- locally compact group; scale function; tidy subgroup; modular function; automorphism
- Identifier
- uon:1510
- Identifier
- http://hdl.handle.net/1959.13/27266
- Identifier
- ISSN:1076-9803
- Full Text
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