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arXiv · 2605.27936

Nuclear Dimension of Twisted $C^*$-Algebras of Virtually Abelian Groups

Forrest Glebe·Pradyut Karmakar·Iason Moutzouris
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Abstract

Let $G$ be a finitely generated virtually abelian group and $[\sigma]\in H^2(G;\mathbb{T})$ such that $\sigma(x,y)$ is always a root of unity. We show that the nuclear dimension of the twisted group $C^*$-algebra $C^*(G,\sigma)$ is equal to the rank of a finite index abelian subgroup of $G$. We also show that $\mbox{dim}_{\text{nuc}}(C^*(\mathbb{Z}^r,\sigma))=r$ if and only if $\sigma$ is type I.

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BibTeXRIS

Forrest Glebe, Pradyut Karmakar, Iason Moutzouris. 2026-05-27. Nuclear Dimension of Twisted $C^*$-Algebras of Virtually Abelian Groups. https://arxiv.org/abs/2605.27936

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