The $K$-theory of the Compact Quantum Group $SU_q(2)$ for $q=-1$

TL;DR

This paper computes the K-theory of the C*-algebra associated with the quantum group SU_q(2) at q=-1 and describes a continuous bundle structure over the interval [-1,0).

Contribution

It provides the first explicit computation of the K-theory for SU_q(2) at q=-1 and constructs a continuous C*-bundle over [-1,0) with fibers isomorphic to C(SU_q(2)).

Findings

K-theory of C(SU_{-1}(2)) is determined.

A continuous C*-bundle over [-1,0) is constructed.

Fibers at q are isomorphic to C(SU_q(2)).

Abstract

We determine the $K$-theory of the $C^{*}$-algebra $C(SU_{-1}(2))$ and describe its spectrum. Moreover, we exhibit a continuous $C^{*}$-bundle over $[-1,0)$ whose fibre at $q$ is isomorphic to $C(SU_{q}(2))$.