Tidy subgroups for commuting automorphisms of totally disconnected groups: an analogue of simultaneous triangularisation of matrices

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
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