Quantum SU(2) and the Baum-Connes conjecture

TL;DR

This paper reviews the proof of the Baum-Connes conjecture for the quantum group SU_q(2) and applies it to compute K-groups of quantum automorphism groups of simple matrix algebras.

Contribution

It provides a detailed review of the Baum-Connes conjecture for SU_q(2) and calculates K-groups for specific quantum automorphism groups, advancing understanding in quantum topology.

Findings

Proof of Baum-Connes conjecture for SU_q(2)

K-groups of quantum automorphism groups determined

Enhanced understanding of quantum group K-theory

Abstract

We review the formulation and proof of the Baum-Connes conjecture for the dual of the quantum group $ SU_q(2) $ of Woronowicz. As an illustration of this result we determine the $ K $-groups of quantum automorphism groups of simple matrix algebras.