标题： 粗空间和一致 Roe 代数的量子化 显示英文标题

标题： A quantization of coarse spaces and uniform Roe algebras

摘要： 我们提出了一种粗空间和一致 Roe 代数的量子化。 这些对象基于 N. Weaver 引入的量子关系，并需要选择一个表示的冯·诺依曼代数。 在对角包含 l_infty(X) ⊂ B(l_2(X)) 的情况下，它们退化为通常的构造。 量子度量空间提供了类似于经典设定的自然例子，但我们也给出了不受度量考虑启发的其他例子，包括新的支持扩张 C*-代数类。 我们还研究了量子粗空间之间映射的基本理论及其对量子一致 Roe 代数的影响。 显示英文摘要

摘要： We propose a quantization of coarse spaces and uniform Roe algebras. The objects are based on the quantum relations introduced by N. Weaver and require the choice of a represented von Neumann algebra. In the case of the diagonal inclusion l_infty(X) subset B(l_2(X)), they reduce to the usual constructions. Quantum metric spaces furnish natural examples parallel to the classical setting, but we provide other examples that are not inspired by metric considerations, including the new class of support expansion C*-algebras. We also work out the basic theory for maps between quantum coarse spaces and their consequences for quantum uniform Roe algebras.