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10 - An Introduction to Totally Disconnected Locally Compact Groups and Their Finiteness Conditions

Published online by Cambridge University Press:  25 November 2023

Edited by
David Jordan ,
Nadia Mazza  and
Sibylle Schroll
David Jordan
Affiliation:
University of Edinburgh
Nadia Mazza
Affiliation:
Lancaster University
Sibylle Schroll
Affiliation:
Universität zu Köln
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Summary

We introduce the theory of totally disconnected locally compact (TDLC) groups, including basic properties of topological groups, a proof of van Dantzig’s theorem and some of the most popular (and trouble-free) examples of TDLC groups. The focus is onTDLC groups that satisfy (homological) finiteness conditions with more emphasis on compact generation: for compactly generated TDLC groups, the notion of the Cayley–Abels graph permits us to deal with the topological group as a geometric object.

Keywords

TDLC groupsfiniteness conditionstopological groups
Type
Chapter
Information
Modern Trends in Algebra and Representation Theory , pp. 335 - 369
Publisher: Cambridge University Press
Print publication year: 2023

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