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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 | References | Similar Articles | Additional Information

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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  • [BK1] B. Blackadar and E. Kirchberg, Generalized inductive limits of finite dimensional C*-algebras, Math. Ann. 307 (1997), 343 - 380. MR 98c:46112
  • [BK2] B. Blackadar and E. Kirchberg, Inner quasidiagonality and strong NF algebras, Preprint.
  • [BKRS] O. Bratteli, A. Kishimoto, M. R$\o$rdam and E. St$\o$rmer, The crossed product of a UHF algebra by a shift, Ergod. Th. Dynam. Sys. 13 (1993), 615 - 626. MR 95c:46111
  • [Br1] N.P. Brown, AF embeddability of crossed products of AF algebras by the integers, J. Funct. Anal. 160 (1998), 150-175. CMP 99:06
  • [Br2] N.P. Brown, Topological Entropy in Exact $C^*$-algebras, Preprint 1998.
  • [Da] K.R. Davidson, $C^{*}$-algebras by Example, Fields Inst. Monographs vol. 6, Amer. Math. Soc., (1996). MR 97i:46095
  • [El] G.A. Elliott, On the classification of $C^*$-algebras of real rank zero, J. reine angew. Math. 443 (1993), 179-219. MR 94i:46074
  • [EE] G.A. Elliott and D.E. Evans, The structure of the irrational rotation $C^*$-algebra, Ann. Math. 138 (1993), 477-501. MR 94j:46066
  • [Ki1] A. Kishimoto, The Rohlin property for automorphisms of UHF algebras, J. reine angew. Math. 465 (1995), 183 - 196. MR 96k:46114
  • [Ki2] A. Kishimoto, Unbounded derivations in $A\mathbb{ T}$ algebras, J. Funct. Anal. 160 (1998), 270-311. CMP 99:06
  • [LP] Q. Lin and N.C. Phillips, Ordered K-theory for $C^*$-algebras of minimal homeomorphisms, Advances in Operator Algebras and Operator Theory, Contem. Math. 228 (1998), 289-314.
  • [Pi] M. Pimsner, Embedding some transformation group C$^{*}$-algebras into AF algebras, Ergod. Th. Dynam. Sys. 3 (1983), 613 - 626. MR 86d:46054
  • [PV] M. Pimsner and D. Voiculescu, Exact sequences for K-groups and Ext-groups of certain crossed products of $C^{*}-algebras$, J. Oper. Th. 4 (1980), 93 - 118. MR 82c:46074
  • [Pu] I. Putnam, On the topological stable rank of certain transformation group C*-algebras, Ergod. Th. and Dyn. Sys. 10 (1990), 197 - 207. MR 91f:46090
  • [Vo1] D. Voiculescu, Almost inductive limit automorphisms and embeddings into AF algebras, Ergod. Th. Dynam. Sys. 6 (1986), 475 - 484. MR 88k:46073
  • [Vo2] D. Voiculescu, Dynamical approximation entropies and topological entropy in operator algebras, Comm. Math. Phys. 170 (1995), 249 - 281. MR 97b:46082

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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

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

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