PreprintCC BY 4.0arXiv
Continuous family of compact quantum metric space structures from cocycle twisted crossed product C∗-algebras
Abstract
We establish the existence of a three-parameter family of compact quantum metric space structures on cocycle twisted crossed products by discrete groups. We are mainly interested in the case where the acting group has exponential/subexponential growth. We prove that the family is jointly continuous with respect to the parameters when the acting group is exact. We obtain quantitative upper and lower bounds for the associated metric dimensions. In particular, the bounds are helpful to prove the failure of lower semicontinuity of the metric dimension with respect to the quantum Gromov-Hausdorff distance. We also prove invariance of metric dimension under zero quantum Gromov-Hausdorff distance.
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BibTeX
@misc{chattopadhyay2026continuous,
title = {{Continuous family of compact quantum metric space structures from cocycle twisted crossed product $\textrmC^\ast$-algebras}},
author = {Arnab Chattopadhyay and Soumalya Joardar},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11316},
eprint = {2609.11316},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11316},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Continuous family of compact quantum metric space structures from cocycle twisted crossed product C^∗-algebras
AU - Arnab Chattopadhyay
AU - Soumalya Joardar
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11316
UR - https://arxiv.org/abs/2609.11316
AB - We establish the existence of a three-parameter family of compact quantum metric space structures on cocycle twisted crossed products by discrete groups. We are mainly interested in the case where the acting group has exponential/subexponential growth. We prove that the family is jointly continuous with respect to the parameters when the acting group is exact. We obtain quantitative upper and lower bounds for the associated metric dimensions. In particular, the bounds are helpful to prove the failure of lower semicontinuity of the metric dimension with respect to the quantum Gromov-Hausdorff distance. We also prove invariance of metric dimension under zero quantum Gromov-Hausdorff distance.
ER -