AF embeddability and topological entropy in noncommutative dynamical systems
Abstract
Let A be an AF C*-algebra and [special characters omitted] be an automorphism. It is shown that the crossed product, [special characters omitted] is AF embeddable if and only if [special characters omitted] compresses no elements of K0( A). If A is UHF then any crossed product by [special characters omitted] is shown to be AF embeddable. In both cases one has good control of the K-theory of the embeddings. A new notion of topological entropy for automorphisms of exact C*-algebras is also introduced. A number of basic results are obtained, but the main entropy result states that if A is exact, [special characters omitted], and [special characters omitted] is the implementing inner automorphism then the topological entropy of α equals that of Adu. Some calculations are also given.
Degree
Ph.D.
Advisors
Dadarlat, Purdue University.
Subject Area
Mathematics
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