论文标题
Bunce-Deddens代数为量子gromov-hausorff圆形代数的距离限制
Bunce-Deddens algebras as quantum Gromov-Hausorff distance limits of circle algebras
论文作者
论文摘要
我们表明，是代数的Bunce-Deddens代数也是Rieffel Quantum Gromov-Hausdorff距离的圆形代数的限制，此外，形成了由Baire Space索引的连续家庭。为此，我们将Bunce-Deddens代数赋予量子公制结构，这一步骤要求我们调和Latremoliere的Gromov-Hausdorff Propinquility和Rieffel的量子Gromov-Hausdorff距离，以便在有序量子量子量子量子空间时。因此，这项工作继续研究了电感限制与度量限制之间的联系。
We show that Bunce-Deddens algebras, which are AT-algebras, are also limits of circle algebras for Rieffel's quantum Gromov-Hausdorff distance, and moreover, form a continuous family indexed by the Baire space. To this end, we endow Bunce-Deddens algebras with a quantum metric structure, a step which requires that we reconcile the constructions of the Latremoliere's Gromov-Hausdorff propinquity and Rieffel's quantum Gromov-Hausdorff distance when working on order-unit quantum metric spaces. This work thus continues the study of the connection between inductive limits and metric limits.
