Hulls and kernels from topological dynamical systems and their applications to homeomorphism C^*-algebras

Abstract

For a topological dynamical system Σ=(X, σ) where σ is a homeomor-phism in an arbitrary compact Hausdorff space X, we consider the noncommutative hulls and kernels with respect to the action σ in the associated C^*-algebra A(Σ). We show that several ideals important for the structure of A(Σ) have the form of such kernels and give topological characterizations of their hulls from the behavior of orbits in the dynamical system.