Separability of group $C^*$-algebras

Question

Let $A$ be the group $C^*$-algebra of free group $F_n$ of rank $n(n\geq 2)$. Is $A$ separable?

Answer 1

Yes. So long as the group $\Gamma$ is countable, both $C^*(\Gamma)$ and $C_r^*(\Gamma)$ will be separable, as in both cases, those elements of $\mathbb C\Gamma$ with coefficients in $\mathbb Q+i\mathbb Q$ will be a countable dense subset.