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

## TL;DR

This paper studies the automorphism groups of Cuntz-Toeplitz algebras, focusing on their homotopy groups, providing new insights into their topological structure and symmetries.

## Contribution

It determines the homotopy groups of automorphism groups of Cuntz-Toeplitz algebras, a novel topological analysis of these operator algebra automorphisms.

## Key findings

- Computed the homotopy groups of automorphism groups
- Identified topological invariants of automorphisms
- Enhanced understanding of Cuntz-Toeplitz algebra symmetries

## Abstract

The Cuntz-Toeplitz algebra $E_{n+1}$ for $n\geq1$ 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.