NC Automorphisms of nc-bounded domains

TL;DR

This paper proves rigidity theorems for noncommutative automorphisms of nc-bounded domains, extending classical results and applying to domains of matrix unit balls, thereby advancing the understanding of noncommutative complex analysis.

Contribution

It introduces new rigidity theorems for nc automorphisms, generalizing classical results and improving recent findings in noncommutative geometry.

Findings

Established uniqueness theorems for nc automorphisms

Extended classical automorphism results to noncommutative settings

Applied results to nc-domains of matrix unit balls

Abstract

We establish rigidity (or uniqueness) theorems for nc automorphisms which are natural extensions of clasical results of H.~Cartan and are improvements of recent results. We apply our results to nc-domains consisting of unit balls of rectangular matrices.