Isomorphism invariants for multivariable \(C^\ast\)-dynamics
type: Item
instance of: scholarly article
title: Isomorphism invariants for multivariable \(C^\ast\)-dynamics
zbMATH Open document ID: 1328.47078
DOI: 10.4171/JNCG/170
author: Evgenios T. A. Kakariadis
author: Elias G. Katsoulis
published in: Journal of Noncommutative Geometry
publication date: 2014-11-12T00:00:00Z
full work available at URL: https://arxiv.org/abs/1210.6068
review text: Let \((A, \alpha)\) be a multivariable \(C^*\)-dynamical system. A family of operator algebras \(\mathrm{alg}(A, \alpha)\) is associated to \((A, \alpha)\) which includes the tensor algebra and the semicrossed product. In this paper, isomorphism invariants for operator algebras associated with multivariable \(C^*\)-dynamical systems are studied. If \((A, \alpha)\) is an automorphic multivariable \(C^*\)-dynamical system, then it induces an homeomorphic multivariable system \((\hat{A}, \hat{\alpha})\) on the spectrum \(\hat{A}\) of \(A\). Let \((A, \alpha)\) and \((B, \beta)\) be automorphic multivariable \(C^*\)-dynamical systems. The main result of the paper is that, if there exist associated operator algebras \(\mathrm{alg}(A, \alpha)\) and \(\mathrm{alg}(B, \beta)\) which are isometrically isomorphic, then the induced multivariable systems \((\hat{A}, \hat{\alpha})\) and \((\hat{B}, \hat{\beta})\) are piecewise conjugate. Several other results of independent interest are also obtained.
Mathematics Subject Classification ID: 47L65
Mathematics Subject Classification ID: 47L75
Mathematics Subject Classification ID: 46L55
Mathematics Subject Classification ID: 46L40
Mathematics Subject Classification ID: 46L89
zbMATH DE Number: 6368719
zbMATH Keywords: \(C^\ast\)-algebra
zbMATH Keywords: dynamical system
zbMATH Keywords: piecewise conjugacy
zbMATH Keywords: Fell spectrum
zbMATH Keywords: outer conjugacy
reviewed by: Mixalis Anoussis
MaRDI profile type: Publication
arXiv ID: 1210.6068
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OpenAlex ID: W2962751508
description: scientific article; zbMATH DE number 6368719