In order to study how the
C∗-algebra C(SμU(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(SμU(3)) better. In this paper, we shall use Bragiel’s
result about the irreducible representations of C(SμU(3)) and the theory
of groupoid C∗-algebras to give an explicit description of the C∗-algebra
structure of C(SμU(3)), which indicates that C(SμU(3)) is some kind of
foliation C∗-algebra of the singular symplectic foliation of the Lie-Poisson group
SU(3).
