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arXiv · 1711.10442

C*-simplicity of HNN extensions and groups acting on trees

Rasmus Sylvester Bryder·Nikolay A. Ivanov·Tron Omland
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Abstract

We study non-ascending HNN extensions acting on their Bass-Serre trees, and characterize C*-simplicity and the unique trace property by means of the kernel and quasi-kernels of the HNN extension in question. We also present a concrete example of an HNN extension that is a new example of a group that is not C*-simple but does have the unique trace property. Additionally, we include certain more general results, mostly based on previous work of various authors, concerning C*-simplicity of groups admitting extreme boundary actions, and in particular, groups acting on trees.

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Rasmus Sylvester Bryder, Nikolay A. Ivanov, Tron Omland. 2019-04-12. C*-simplicity of HNN extensions and groups acting on trees. https://arxiv.org/abs/1711.10442

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