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

2017/11/28 by Rasmus Sylvester Bryder, Bryder, Rasmus Sylvester, Nikolay A. Ivanov +3 · 1 citation
Mathematics · #20E06 (Primary) 46L05 #20E08 (Secondary) #22D25 #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1711.10442

openalex publication_date 2017/11/28 · openalex created_date 2021/04/26 · openalex updated_date 2026/07/28

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.

Cited by

• Proximality and selflessness for group C*-algebras

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