Crossed products of type I AF algebras by Abelian groups
type: Item
instance of: scholarly article
title: Crossed products of type I AF algebras by Abelian groups
zbMATH Open document ID: 0646.46062
DOI: 10.1007/BF02782937
author: Elliot C. Gootman
author: Aldo J. Lazar
published in: Israel Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: Let \((G,A,\alpha)\) be a separable \(C^*\)-dynamical system, with \(G\) abelian, and let \(\Gamma\) denote the dual group of \(G\). We characterize the \(\Gamma\)-invariant ideals of the crossed product algebra \(G\times_{\alpha} A\), and use this characterization to prove that if in addition \(G\) is compact and \(A\) is type I AF, then \(G\times_{\alpha} A\) is AF also. Finally, assuming \(G\) is discrete abelian and both \(A\) and \(G\times_{\alpha} A\) are type I, we determine necessary and sufficient conditions in terms of \(A\) and the isotropy subgroups for the action of \(G\) on \(\hat A\), for \(G\times_{\alpha} A\) to be AF.
Mathematics Subject Classification ID: 46L55
Mathematics Subject Classification ID: 46L35
Mathematics Subject Classification ID: 22D35
zbMATH DE Number: 4054347
zbMATH Keywords: separable \(C^*\)-dynamical system
zbMATH Keywords: dual group
zbMATH Keywords: crossed product
zbMATH Keywords: isotropy subgroups
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4054347