Invariant $C^*$-subalgebras of the reduced group $C^*$-algebra
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917360248553472 |
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| author | Amrutam, Tattwamasi Jiang, Yongle |
| author_facet | Amrutam, Tattwamasi Jiang, Yongle |
| contents | Let $Γ$ be a countable discrete group. We say that $Γ$ has $C^*$-invariant subalgebra rigidity (ISR) property if every $Γ$-invariant $C^*$-subalgebra $\mathcal{A}\le C_r^*(Γ)$ is of the form $C_r^*(N)$ for some normal subgroup $N\triangleleftΓ$. We show that all torsion-free, non-amenable (cylindrically) hyperbolic groups with property-AP and a finite direct product of such groups have this property. We also prove that an infinite group $Γ$ has the C$^*$-ISR property only if $Γ$ is simple amenable or $C^*$-simple. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_09548 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Invariant $C^*$-subalgebras of the reduced group $C^*$-algebra Amrutam, Tattwamasi Jiang, Yongle Operator Algebras Dynamical Systems Functional Analysis Let $Γ$ be a countable discrete group. We say that $Γ$ has $C^*$-invariant subalgebra rigidity (ISR) property if every $Γ$-invariant $C^*$-subalgebra $\mathcal{A}\le C_r^*(Γ)$ is of the form $C_r^*(N)$ for some normal subgroup $N\triangleleftΓ$. We show that all torsion-free, non-amenable (cylindrically) hyperbolic groups with property-AP and a finite direct product of such groups have this property. We also prove that an infinite group $Γ$ has the C$^*$-ISR property only if $Γ$ is simple amenable or $C^*$-simple. |
| title | Invariant $C^*$-subalgebras of the reduced group $C^*$-algebra |
| topic | Operator Algebras Dynamical Systems Functional Analysis |
| url | https://arxiv.org/abs/2503.09548 |