The structure of twisted \(SU(3)\) groups (Q749687)

In order to study how the \(C^*\)-algebra \(C(S_{\mu}U(3))\) of twisted SU(3) groups introduced by Woronowicz is related to the deformation quantization of the Lie-Poisson SU(3), we need to understand the algebraic structure of \(C(S_{\mu}U(3))\) better. In this paper, we use Bragiel's result about the irreducible representations of \(C(S_{\mu}U(3))\) and the theory of groupoid \(C^*\)-algebras to give an explicit description of the \(C^*\)-algebra structure of \(C(S_{\mu}U(3))\), which indicates that \(C(S_{\mu}U(3))\) is some kind of foliation \(C^*\)-algebra of the singular symplectic foliation of the Lie-Poisson group SU(3).