论文标题
Gromov-Hausdorff量化间隔的收敛性
Gromov-Hausdorff convergence of quantised intervals
论文作者
论文摘要
量子球S^2_q允许具有频谱{0} \ cup {q^{2k}的自然交换C*-subalgebra I_Q：k = 0,1,2，...}，因此可以被视为经典间隔的定量版本。我们在这里研究了从S^2_Q上的相应结构继承的I_Q上的紧凑型量子度量空间结构，并为频谱上诱导的度量的公式提供了明确的公式。此外，我们表明，所得的度量空间在变形参数q中相对于gromov-hausdorff距离持续变化，并且它们会收敛到经典的长度间隔，因为Q趋向于1。
The Podles quantum sphere S^2_q admits a natural commutative C*-subalgebra I_q with spectrum {0} \cup {q^{2k}: k = 0,1,2,...}, which may therefore be considered as a quantised version of a classical interval. We study here the compact quantum metric space structure on I_q inherited from the corresponding structure on S^2_q, and provide an explicit formula for the metric induced on the spectrum. Moreover, we show that the resulting metric spaces vary continuously in the deformation parameter q with respect to the Gromov-Hausdorff distance, and that they converge to a classical interval of length pi as q tends to 1.
