Topological entropy, embeddings and unitaries in nuclear quasidiagonal -algebras

Author:
Nathanial P. Brown

Journal:
Proc. Amer. Math. Soc. **128** (2000), 2603-2609

MSC (1991):
Primary 46L05, 46L80, 46L55

DOI:
https://doi.org/10.1090/S0002-9939-00-05329-6

Published electronically:
March 1, 2000

MathSciNet review:
1664305

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Using topological entropy of automorphisms of -algebras, it is shown that some important facts from the theory of AF algebras do not carry over to the class of 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 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:
https://doi.org/10.1090/S0002-9939-00-05329-6

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