Operator algebra quantum homogeneous spaces of universal gauge groups

TL;DR

This paper develops a framework for quantizing universal gauge groups like SU(∞) and their homogeneous spaces using sigma-C*-algebras, and computes their K-theory, advancing the mathematical understanding of quantum gauge symmetries.

Contribution

It introduces concise definitions of sigma-C*-quantum groups and homogeneous spaces, and applies these to universal gauge groups, including K-theory computations.

Findings

Defined sigma-C*-quantum groups and spaces.

Quantized universal gauge groups such as SU(∞).

Computed K-theory for quantum homogeneous spaces.

Abstract

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).