Nuclear Dimension of Twisted $C^*$-Algebras of Virtually Abelian Groups
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914606881964032 |
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| author | Glebe, Forrest Karmakar, Pradyut Moutzouris, Iason |
| author_facet | Glebe, Forrest Karmakar, Pradyut Moutzouris, Iason |
| contents | Let $G$ be a finitely generated virtually abelian group and $[σ]\in H^2(G;\mathbb{T})$ such that $σ(x,y)$ is always a root of unity. We show that the nuclear dimension of the twisted group $C^*$-algebra $C^*(G,σ)$ is equal to the rank of a finite index abelian subgroup of $G$. We also show that $\mbox{dim}_{\text{nuc}}(C^*(\mathbb{Z}^r,σ))=r$ if and only if $σ$ is type I. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_27936 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Nuclear Dimension of Twisted $C^*$-Algebras of Virtually Abelian Groups Glebe, Forrest Karmakar, Pradyut Moutzouris, Iason Operator Algebras Group Theory Representation Theory 22D10, 22D25, 46L05 Let $G$ be a finitely generated virtually abelian group and $[σ]\in H^2(G;\mathbb{T})$ such that $σ(x,y)$ is always a root of unity. We show that the nuclear dimension of the twisted group $C^*$-algebra $C^*(G,σ)$ is equal to the rank of a finite index abelian subgroup of $G$. We also show that $\mbox{dim}_{\text{nuc}}(C^*(\mathbb{Z}^r,σ))=r$ if and only if $σ$ is type I. |
| title | Nuclear Dimension of Twisted $C^*$-Algebras of Virtually Abelian Groups |
| topic | Operator Algebras Group Theory Representation Theory 22D10, 22D25, 46L05 |
| url | https://arxiv.org/abs/2605.27936 |