Non-Abelian factors for actions of Z and other non-C-simple groups

Tattwamasi Amrutam, Eli Glasner, Yair Glasner

Research output: Contribution to journalArticlepeer-review


Let Γ be a countable group and (X,Γ) a compact topological dynamical system. We study the question of the existence of an intermediate C-subalgebra A Cr(Γ)<A<C(X)⋊rΓ, which is not of the form A=C(Y)⋊rΓ, corresponding to a factor map (X,Γ)→(Y,Γ). Here Cr(Γ) is the reduced C-algebra of Γ and C(X)⋊rΓ is the reduced C-crossed-product of (X,Γ). Our main results are: (1) For Γ which is not C-simple, when (X,Γ) admits a Γ-invariant probability measure, then such a sub-algebra always exists. (2) For Γ=Z and (X,Γ) an irrational rotation of the circle X=R/Z, we give a full description of all these non-crossed-product subalgebras.

Original languageEnglish
Article number110456
JournalJournal of Functional Analysis
Issue number2
StatePublished - 15 Jul 2024


  • C-crossed products
  • C-simple groups
  • Intermediate subalgebras
  • Irrational rotation crossed product

ASJC Scopus subject areas

  • Analysis


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