Noncommutative hyperbolic metrics

2017/07/31 by Serban T. Belinschi, Serban Belinschi, Victor Vinnikov +2 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebra over a field #Algebraic number #Discrete mathematics #Equivalence (formal languages) #FOS: Mathematics #Holomorphic and Operator Theory #Holomorphic function #Mathematical analysis #Mathematics #Noncommutative algebraic geometry #Noncommutative geometry #Noncommutative quantum field theory #Operator Algebras (math.OA) #Pure mathematics #math.OA

paper · pdf · doi:10.48550/arxiv.1707.09762

Second version: expanded introduction, several modifications, including the definition of a new distance, a correction in Proposition 4.7, and a strengthening of the free probability results. Comments welcome

openalex publication_date 2017/07/31 · arxiv created 2019/10/14 · arxiv updated 2019/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We characterize certain noncommutative domains in terms of noncommutative holomorphic equivalence via a pseudometric that we define in purely algebraic terms. We prove some properties of this pseudometric and provide an application to free probability.

Citations

• Spectral properties of polynomials in independent Wigner and deterministic matrices

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