Operator algebra quantum groups of universal gauge groups

TL;DR

This paper introduces a new framework for quantizing universal gauge groups like SU(∞) using sigma-C*-algebras, expanding the mathematical understanding of quantum groups in this setting.

Contribution

It defines sigma-C*-quantum groups and situates them within the context of countably compactly generated groups and C*-compact quantum groups, providing a concise new approach.

Findings

Proposes a concise definition of sigma-C*-quantum groups.

Connects sigma-C*-quantum groups with countably compactly generated groups.

Links the concept to C*-compact quantum groups.

Abstract

In this paper, we quantize universal gauge groups such as SU(\infty), in the sigma-C*-algebra setting. More precisely, we propose a concise definition of sigma-C*-quantum groups and explain the concept here. At the same time, we put this definition in the mathematical context of countably compactly generated groups as well as C*-compact quantum groups.