The homotopy groups of the automorphism groups of Cuntz-Toeplitz algebras

The Cuntz-Toeplitz algebra $E_{n+1}$ for $n\ge 1$ is the universal C*-algebra generated by $n+1$ isometries with mutually orthogonal ranges. In this paper, we investigate the automorphism groups of the Cuntz-Toeplitz algebras and determine their homotopy groups.