On the permanence properties of residually exact groups
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915675801387008 |
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| author | Awazu, Hikaru |
| author_facet | Awazu, Hikaru |
| contents | A discrete group $Γ$ is called exact if the reduced group C*-algebra ${C_λ}^{*}(Γ)$ is exact as C*-algebras, and a discrete group $Λ$ is called residually exact if every nonunital element $g \in Λ$ admits a surjective group homomorphism from $Λ$ to some exact group $Γ$ which maps $g$ to a nonunital element of $Γ$.
We prove the class of residually exact groups is closed under taking Green's graph products [1], double amalgamed products and special HNN extensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_13212 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the permanence properties of residually exact groups Awazu, Hikaru Group Theory Operator Algebras A discrete group $Γ$ is called exact if the reduced group C*-algebra ${C_λ}^{*}(Γ)$ is exact as C*-algebras, and a discrete group $Λ$ is called residually exact if every nonunital element $g \in Λ$ admits a surjective group homomorphism from $Λ$ to some exact group $Γ$ which maps $g$ to a nonunital element of $Γ$. We prove the class of residually exact groups is closed under taking Green's graph products [1], double amalgamed products and special HNN extensions. |
| title | On the permanence properties of residually exact groups |
| topic | Group Theory Operator Algebras |
| url | https://arxiv.org/abs/2512.13212 |