Biholomorphisms of the unit ball of Cⁿ and semicrossed products

2009/04/19 by Kenneth R. Davidson, K. R. Davidson, Davidson, K. R. +3
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Mathematics and Applications #Operator Algebras (math.OA) #math.FA #math.OA

paper · pdf · doi:10.48550/arxiv.0904.2876

14 pages

arxiv created 2009/04/19 · openalex publication_date 2009/04/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Assume that ϕ₁ and ϕ₂ are automorphisms of the non-commutative disc algebra \fA_n, n ≥ 2. We show that the semicrossed products \fA_n ×_ϕ1 \bZ⁺ and \fA_n ×_ϕ2 \bZ⁺ are isomorphic as algebras if and only if ϕ₁ and ϕ₂ are conjugate via an automorphism of \fA_n. A similar result holds for semicrossed products of the d-shift algebra \A_d, d ≥ 2.

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