PreprintCC BY 4.0arXiv
Nuclear Dimension of Twisted C*-Algebras of Virtually Abelian Groups
Abstract
Let G be a finitely generated virtually abelian group and [Ο]β H2(G;π) such that Ο(x,y) is always a root of unity. We show that the nuclear dimension of the twisted group C*-algebra C*(G,Ο) is equal to the rank of a finite index abelian subgroup of G. We also show that dimnuc(C*(β€r,Ο))=r if and only if Ο is type I.
Related
- The Nuclear Dimension of Extensions and Graph C*-Algebras
- Virtually Gorenstein Artin algebras are weakly Gorenstein
- Wedderburn decomposition of Twisted skew abelian group algebra
- Twisted Deligne modules and abelian varieties over finite fields
- Binomial Artin-Schelter Regular Algebras and Twisted Monoid Algebras
BibTeX
@misc{glebe2026nuclear,
title = {{Nuclear Dimension of Twisted $C^*$-Algebras of Virtually Abelian Groups}},
author = {Forrest Glebe and Pradyut Karmakar and Iason Moutzouris},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.27936},
eprint = {2605.27936},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.27936},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Nuclear Dimension of Twisted C^*-Algebras of Virtually Abelian Groups
AU - Forrest Glebe
AU - Pradyut Karmakar
AU - Iason Moutzouris
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2605.27936
UR - https://arxiv.org/abs/2605.27936
AB - Let G be a finitely generated virtually abelian group and [Ο]β H^2(G;π) such that Ο(x,y) is always a root of unity. We show that the nuclear dimension of the twisted group C^*-algebra C^*(G,Ο) is equal to the rank of a finite index abelian subgroup of G. We also show that dim_nuc(C^*(β€^r,Ο))=r if and only if Ο is type I.
ER -