Ashot Minasyan

Property P_nai and C^*-simplicity of 1-relator groups

A group is said to be C^*-simple if its reduced C^*-algebra has no two-sided ideals. I will discuss a characterisation of C^*-simplicity for finitely generated groups with one defining relator which goes via the property P_nai of Bekka, Cowling and de la Harpe. This “naïve” property was one of the first criteria for C^*-simplicity of a group G and can be stated as follows: for every finite collection of non-trivial elements g₁,…,g_k∈G there exists an infinite order element f∈G such that the subgroup ⟨g_i,f⟩ is naturally isomorphic to the free product ⟨g_i⟩∗⟨f⟩, for each i=1,...,k. The talk will be based on joint work with Motiejus Valiunas.