Classification of Noncommutative Domain Algebras

TL;DR

This paper provides a comprehensive classification of noncommutative domain algebras, extending the understanding of their structure by leveraging techniques from multivariate complex analysis and biholomorphic equivalence.

Contribution

It introduces a complete classification framework for noncommutative domain algebras using methods inspired by complex analysis and domain equivalence.

Findings

Classification based on biholomorphic equivalence of domains

Extension of Hardy algebra concepts to noncommutative setting

Framework applicable to multivariate noncommutative function theory

Abstract

Noncommutative domain algebras are noncommutative analogues of the algebras of holomorphic functions on domains of $\C^n$ defined by holomorphic polynomials, and they generalize the noncommutative Hardy algebras. We present here a complete classification of these algebras based upon techniques inspired by multivariate complex analysis, and more specifically the classification of domains in hermitian spaces up to biholomorphic equivalence.