View paper:

pdf

dvi

ps

View abstract:

pdf	gif
links page

Graphical interface

Volume 10

Other volumes

Full text search of NYJM papers

NYJM home

Published:	January 7, 2004
Keywords:	locally compact group, scale function, tidy subgroup, modular function, automorphism
Subject:	Primary 22D05; Secondary 22D45, 20E25, 20E36

Abstract:

Let $\alpha$ be an automorphism of the totally disconnected group $G$. The compact open subgroup, $V$, of $G$ is \emph{tidy} for $\alpha$ if $[\alpha(V') : \alpha(V')\cap V']$ is minimised at $V$, where $V'$ ranges over all compact open subgroups of $G$. Identifying a subgroup tidy for $\alpha$ 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.

Acknowledgments: Research supported by A.R.C. Grant A69700321 Author information: School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, NSW 2308, Australia george@frey.newcastle.edu.au