Connectedness and irreducibility of compact quantum groups

TL;DR

This paper explores the relationship between connectedness and irreducibility in compact quantum groups, establishing that irreducibility implies connectedness and examining the converse in relation to Kaplansky's conjectures.

Contribution

It introduces a natural notion of irreducibility in compact quantum groups and investigates its implications for connectedness and related algebraic conjectures.

Findings

Irreducibility implies connectedness in compact quantum groups

The converse relation is linked to Kaplansky's conjectures

Provides insights into the structure of quantum groups

Abstract

We show that a natural notion of irreducibility implies connectedness in the Compact Quantum Group setting. We also investigate the converse implication and show it is related to Kaplansky's conjectures on group algebras.