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The non-amenability criterion for simplicity of the reduced $C^*$ -algebra of Thompson's group $T$
Non-amenability criterion. If $F$ is non-amenable, then $T$ does not admit a normalish amenable subgroup, and consequently the reduced $C^*$ -algebra of $T$ is simple.
Conjectureopenc-star-simplicity group-theory thompson-groupsarXiv posted 2 days ago

The non-amenability criterion for simplicity of the reduced C∗C^*C∗-algebra of Thompson's group TTT