Operator Algebra Quantum Homogeneous Spaces of Universal Gauge Groups

In this paper, we quantize universal gauge groups such as SU(∞), as well as their homogeneous spaces, in the σ-C*-algebra setting. More precisely, we propose concise definitions of σ-C*-quantum groups and σ-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 these groups for the quantum homogeneous spaces associated to the quantum version of the universal gauge group SU(∞).