泛规范群的算子代数量子齐性空间
Operator algebra quantum homogeneous spaces of universal gauge groups
摘要：
本文在sigma-C ~*-代数的框架下研究了SU（\infty）等普适规范群及其齐性空间。更准确地说，我们提出了sigma-C*-量子群和sigma-C*-量子齐性空间的简明定义，并在这里解释了这些概念。同时，我们把这些定义放在可数紧生成空间以及C*-紧量子群和齐性空间的数学背景中。我们还研究了这些空间的可表示的K-理论，并计算了与普适规范群SU（\infty）相关的量子齐性空间的K-理论。
英文摘要：
In this paper, we quantize universal gauge groups such as SU(\infty), as well as their homogeneous spaces, in the sigma-C*-algebra setting. More precisely, we propose concise definitions of sigma-C*-quantum groups and sigma-C*-quantum homogeneous spaces and explain these concepts here. At the same time, we put these definitions in the mathematical context of countably compactly generated spaces as well as C*-compact quantum groups and homogeneous spaces. We also study the representable K-theory of these spaces and compute it for the quantum homogeneous spaces associated to the universal gauge group SU(\infty).
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