C*-simplicity of relative profinite completions of generalized Baumslag-Solitar groups

Miho Mukohara

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arXiv · 2201.11347

C*-simplicity of relative profinite completions of generalized Baumslag-Solitar groups

Miho Mukohara

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Abstract

Suzuki recently gave constructions of non-discrete examples of locally compact C*-simple groups and Raum showed C*-simplicity of the relative profinite completions of the Baumslag-Solitar groups by using Suzuki's results. We extend this result to some fundamental groups of graphs of groups called generalized Baumslag-Solitar groups. In this article, we focus on some sufficient condition to show that these locally compact groups are C*-simple and that KMS-weights of these reduced group C*-algebras are unique. This condition is an analogue of the Powers averaging property of discrete groups and holds for several currently known constructions of non-discrete C*-simple groups.

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Miho Mukohara. 2022-01-27. C*-simplicity of relative profinite completions of generalized Baumslag-Solitar groups. https://arxiv.org/abs/2201.11347

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