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arXiv · 1605.06395

C*-simplicity of free products with amalgamation and radical classes of groups

Nikolay A. Ivanov·Tron Omland
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Abstract

We give new characterizations to ensure that a free product of groups with amalgamation has a simple reduced group C*-algebra, and provide a concrete example of an amalgam with trivial kernel, such that its reduced group C*-algebra has a unique tracial state, but is not simple. Moreover, we show that there is a radical class of groups for which the reduced group C*-algebra of any group is simple precisely when the group has a trivial radical corresponding to this class.

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Nikolay A. Ivanov, Tron Omland. 2016-05-20. C*-simplicity of free products with amalgamation and radical classes of groups. https://doi.org/10.1016/j.jfa.2016.12.011

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