C*-simplicity and the amenable radical
Abstract
A countable group is C*-simple if its reduced C*-algebra is simple. It is well known that C*-simplicity implies that the amenable radical of the group must be trivial. We show that the converse does not hold by constructing explicit counter-examples. We additionally prove that every countable group embeds into a countable group with trivial amenable radical and that is not C*-simple.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2015
- DOI:
- 10.48550/arXiv.1507.03452
- arXiv:
- arXiv:1507.03452
- Bibcode:
- 2015arXiv150703452L
- Keywords:
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- Mathematics - Group Theory;
- Mathematics - Operator Algebras
- E-Print:
- The previous versions of this article were entitled "Discrete groups that are not C*-simple". The results have been strengthened and Theorem D has been added