On generators of $\mathrm{C}_r^*(\mathbb{F}_2)$

Abstract

It is shown that the reduced group C*-algebra $\mathrm{C}_r^*(\mathbb{F}_2)$ is singly generated, where $\mathbb F_2$ is the free group on two generators. With respect to the generator constructed in the paper, the topological free entropy dimension of $\mathrm{C}_r^*(\mathbb{F}_2)$ is shown to be $2$.