I have a question about an irreducible representation of the (full) group $C^*$-algebra of an infinite dihedral group $D_\infty$, denoted by $C^*(D_\infty)$
Ultimately, I'm interested in finding a primitive ideal space of $C^*(D_\infty)$ which is the kernel of irreducible representation of $C^*(D_\infty)$.
But I'm having a hard time finding it.
Should I find pure states on $C^*(D_\infty)$ first since they correspond to irreducible representations of $C^*(D_\infty)$?
Any reference will be appreciated.
Hope there is someone who's familiar with these stuff and thank you in advance.