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

Willis, George A. (2004) Tidy subgroups for commuting automorphisms of totally disconnected groups: an analogue of simultaneous triangularisation of matrices. New York Journal of Mathematics, 10 .

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Abstract

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.

Item Type: Article
Uncontrolled Keywords: locally compact group, scale function, tidy subgroup, modular function, automorphism
Subjects: UNSPECIFIED
Faculty: UNSPECIFIED
Depositing User: Dr David Allingham
Date Deposited: 28 Sep 2012 12:05
Last Modified: 28 Sep 2012 12:05
URI: https://docserver.carma.newcastle.edu.au/id/eprint/1190

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