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

Brown, Nathanial

doi:10.1090/S0002-9939-00-05329-6

Topological entropy, embeddings and unitaries in nuclear quasidiagonal $C^*$-algebras
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by Nathanial P. Brown PDF

Proc. Amer. Math. Soc. 128 (2000), 2603-2609 Request permission

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 $A\mathbb {T}$ 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 injective homomorphisms from a building block into an $A\mathbb {T}$ algebra need not differ by an (inner) automorphism when they agree on K-theory.

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