2014/09/17 by Christopher Bronk Ramsey, Christopher Ramsey, Ramsey, Christopher · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Nonlinear Waves and Solitons #Operator Algebras (math.OA) #math.DS #math.OA
paper · pdf · doi:10.48550/arxiv.1409.5109
21 pages, final version, accepted to Indiana U. J. of Math
openalex publication_date 2014/09/17 · arxiv created 2015/06/30 · arxiv updated 2015/07/01 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
We examine the completely isometric automorphisms of a free product of noncommutative disc algebras. It will be established that such an automorphism is given simply by a completely isometric automorphism of each component of the free product and a permutation of the components. This mirrors a similar fact in topology concerning biholomorphic automorphisms of product spaces with nice boundaries due to Rudin, Ligocka and Tsyganov. This paper is also a study of multivariable dynamical systems by their semicrossed product algebras. A new form of dynamical system conjugacy is introduced and is shown to completely characterize the semicrossed product algebra. This is proven by using the rigidity of free product automorphisms established in the first part of the paper. Lastly, a representation theory is developed to determine when the semicrossed product algebra and the tensor algebra of a dynamical system are completely isometrically isomorphic.