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January 25, 2026American Journal of Mathematics0 citations

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

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YSYuhei Suzuki

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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Cite This Study

Yuhei Suzuki (2026) studied this question.

synapsesocial.com/papers/6975b1a9feba4585c2d6d2d8https://doi.org/10.1353/ajm.2026.a980768
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