AF embeddability and topological entropy in noncommutative dynamical systems
Let A be an AF C*-algebra and a∈AutA be an automorphism. It is shown that the crossed product, A⋊aZ, is AF embeddable if and only if a* compresses no elements of K0( A). If A is UHF then any crossed product by Zn 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, a∈AutA , and Adu∈Aut A⋊aZ is the implementing inner automorphism then the topological entropy of α equals that of Adu. Some calculations are also given. ^
Major Professor: Marius Dadarlat, Purdue University.