English

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

Operator Algebras 2026-05-28 v1 Group Theory Representation Theory

Abstract

Let GG be a finitely generated virtually abelian group and [σ]H2(G;T)[\sigma]\in H^2(G;\mathbb{T}) such that σ(x,y)\sigma(x,y) is always a root of unity. We show that the nuclear dimension of the twisted group CC^*-algebra C(G,σ)C^*(G,\sigma) is equal to the rank of a finite index abelian subgroup of GG. We also show that \mboxdimnuc(C(Zr,σ))=r\mbox{dim}_{\text{nuc}}(C^*(\mathbb{Z}^r,\sigma))=r if and only if σ\sigma is type I.

Keywords

Cite

@article{arxiv.2605.27936,
  title  = {Nuclear Dimension of Twisted $C^*$-Algebras of Virtually Abelian Groups},
  author = {Forrest Glebe and Pradyut Karmakar and Iason Moutzouris},
  journal= {arXiv preprint arXiv:2605.27936},
  year   = {2026}
}