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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Author: Nathanial P. Brown
Journal: Proc. Amer. Math. Soc. 128 (2000), 2603-2609
MSC (1991): Primary 46L05, 46L80, 46L55
Published electronically: March 1, 2000
MathSciNet review: 1664305
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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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Additional Information

Nathanial P. Brown
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-1901
Address at time of publication: Department of Mathematics, University of California-Berkeley, Berkeley, California 94720
Email: nbrown@math.purdue.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05329-6
PII: S 0002-9939(00)05329-6
Keywords: Topological entropy, (generalized) inductive limits, inner automorphisms, embeddings
Received by editor(s): October 14, 1998
Published electronically: March 1, 2000
Additional Notes: This work was partially supported by an NSF Dissertation Enhancement Award
Communicated by: David R. Larson
Article copyright: © Copyright 2000 American Mathematical Society