On the Haar measure of the quantum \(SU(N)\) group (Q1803530)

Let \(C(SU_{\mu}(N))\) denote the compact quantum group of type \(SU(N)\), that is, the \(C^*\)-algebra which is the completion of the algebra of rational functions on the quantum \(SL(N)\) with respect to a suitable norm. It is proved that the Haar measure \(\phi\) on \(C(SU_{\mu}(N))\) is faithful, i.e. that \(\phi(a^* a)\leq 0\) if \(a\in C(SU_{\mu}(N))-0\).