Toeplitz algebras associated to isometric flows
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 \(\Phi\).
scientific article; zbMATH DE number 1029003