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

Abstract

It is shown that the reduced group C*-algebra ${\mathrm{C}}_r^{\ast }({\mathbb{F}}_2)$ 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 ${\mathrm{C}}_r^{\ast }({\mathbb{F}}_2)$ is shown to be $2$.

15 pages. The generator and the computation of topological free entropy dimension were obtained by ChatGPT