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DECOMPOSITION THEOREMS FOR AUTOMORPHISM GROUPS OF TREES

Part of: Locally compact groups and their algebras Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  20 May 2020

MAX CARTER Open the ORCID record for MAX CARTER [Opens in a new window]  and
GEORGE A. WILLIS Open the ORCID record for GEORGE A. WILLIS [Opens in a new window]
MAX CARTER
Affiliation:
School of Mathematical and Physical Sciences,University of Newcastle, Callaghan, New South Wales, Australia email max.carter@newcastle.edu.au
GEORGE A. WILLIS*
Affiliation:
School of Mathematical and Physical Sciences,University of Newcastle, Callaghan, New South Wales, Australia email george.willis@newcastle.edu.au
*
✉george.willis@newcastle.edu.au
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Abstract

Motivated by the Bruhat and Cartan decompositions of general linear groups over local fields, we enumerate double cosets of the group of label-preserving automorphisms of a label-regular tree over the fixator of an end of the tree and over maximal compact open subgroups. This enumeration is used to show that every continuous homomorphism from the automorphism group of a label-regular tree has closed range.

Keywords

groups acting on treesautomorphism groupregular treelabel-regular treeLie group decomposition

MSC classification

Primary: 20E08: Groups acting on trees
Secondary: 22D05: General properties and structure of locally compact groups
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 103 , Issue 1 , February 2021 , pp. 104 - 112
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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Footnotes

This research was supported by the Australian Research Council grant FL170100032.

References

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