What question did this study set out to answer?

To demonstrate that every countable group can act amenably on stably finite simple C∗-algebras.

January 25, 2026

Every countable group admits amenable actions on stably finite simple C∗-algebras

Key Points

To demonstrate that every countable group can act amenably on stably finite simple C∗-algebras.
Construct amenable actions using full Fock space of regular representation.
Employ trace-scaling automorphism for the construction.
Presented explicit examples of non-amenable groups acting amenably.
Confirmed the existence of such actions for any countable group.

Abstract

abstract: We give the first examples of (non-amenable group) amenable actions on stably finite simple C^-algebras. More precisely, we give such actions for any countable group in an explicit way. The main ingredients of our construction are the full Fock space of the regular representation and a trace-scaling automorphism.

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