## Abstract

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 C_{r}^{⁎}(Γ)<A<C(X)⋊_{r}Γ, which is not of the form A=C(Y)⋊_{r}Γ, corresponding to a factor map (X,Γ)→(Y,Γ). Here C_{r}^{⁎}(Γ) is the reduced C^{⁎}-algebra of Γ and C(X)⋊_{r}Γ 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 language | American English |
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Article number | 110456 |

Journal | Journal of Functional Analysis |

Volume | 287 |

Issue number | 2 |

DOIs | |

State | Published - 15 Jul 2024 |

## Keywords

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

## All Science Journal Classification (ASJC) codes

- Analysis

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