Toeplitz algebras associated to isometric flows
type: Item
instance of: scholarly article
title: Toeplitz algebras associated to isometric flows
zbMATH Open document ID: 0874.58068
author: Efton Park
published in: Illinois Journal of Mathematics
publication date: 1997-07-03T00:00:00Z
review text: Let \(M\) be a compact Riemannian manifold, and let \(\Phi=\{\phi_t\}\) be an isometric flow on \(M\). In this paper, the author associates a Toeplitz algebra \(T(\Phi)\) to \(\Phi\) and studies how the \(C^*\)-algebraic properties of \(T(\Phi)\) are related to the topological and geometric properties of \(\Phi\). By restricting \(\Phi\) to each of its orbit closures, one obtains a family of Toeplitz algebras, and the author shows that these Toeplitz algebras form a continuous field of \(C^*\)-algebras. In addition, it is proved that \(T(\Phi)\) is naturally isomorphic to the \(C^*\)-algebra of continuous sections of this field. The author uses this result to show that \(T(\Phi)\) depends only on the topological properties of \(\Phi\).
Mathematics Subject Classification ID: 37C10
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 46M20
zbMATH DE Number: 1029003
zbMATH Keywords: isometric flows
zbMATH Keywords: continuous fields of \(C^*\)-algebras
zbMATH Keywords: Toeplitz algebra
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1029003