发表机构
Indian Institute of Science Education And Research Kolkata（印度科学教育研究所加尔各答分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在离散群余环扭曲交叉积上构造了三参数紧量子度量空间结构族，证明其联合连续性并给出度量维数定量界，揭示了维数关于量子Gromov-Hausdorff距离的下半连续性失效及零距离下维数不变性。
AI 中文摘要
我们建立了离散群余环扭曲交叉积上三参数紧量子度量空间结构族的存在性。我们主要关注作用群具有指数/次指数增长的情形。我们证明了当作用群是精确群时，该族关于参数是联合连续的。我们获得了相关度量维数的定量上下界。特别地，这些界有助于证明度量维数关于量子Gromov-Hausdorff距离的下半连续性的失效。我们还证明了在零量子Gromov-Hausdorff距离下度量维数的不变性。
英文摘要
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.
Comments35 pages
