Adrien Le Boudec
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 countable groups without non-trivial amenable normal subgroups and that are not C*-simple.
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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 countable groups without non-trivial amenable normal subgroups and that are not C*-simple.
Key concepts: Countable set, Converse, Simple (philosophy), Simplicity, Mathematics, Group (periodic table), Simple group, Pure mathematics