Topological entropy, embeddings and unitaries in nuclear quasidiagonal $C^*$-algebras

Abstract

Using topological entropy of automorphisms of C*-algebras, it is shown that some important facts from the theory of AF algebras do not carry over to the class of AT algebras. It is shown that in general one cannot perturb a basic building block into a larger one which almost contains it. The same entropy obstruction used to prove this fact also provides a new obstruction to the known fact that two invective homomorphisms from a building block into an AT algebra need not differ by an (inner) automorphism when they agree on K-theory.