Topological entropy, embeddings and unitaries in nuclear quasidiagonal algebras
Author:
Nathanial P. Brown
Journal:
Proc. Amer. Math. Soc. 128 (2000), 26032609
MSC (1991):
Primary 46L05, 46L80, 46L55
Published electronically:
March 1, 2000
MathSciNet review:
1664305
Fulltext PDF Free Access
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References 
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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 Ktheory.
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 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. Rrdam and E. Strmer, 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), 150175. CMP 99:06
 [Br2]
 N.P. Brown, Topological Entropy in Exact algebras, Preprint 1998.
 [Da]
 K.R. Davidson, algebras by Example, Fields Inst. Monographs vol. 6, Amer. Math. Soc., (1996). MR 97i:46095
 [El]
 G.A. Elliott, On the classification of algebras of real rank zero, J. reine angew. Math. 443 (1993), 179219. MR 94i:46074
 [EE]
 G.A. Elliott and D.E. Evans, The structure of the irrational rotation algebra, Ann. Math. 138 (1993), 477501. 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 algebras, J. Funct. Anal. 160 (1998), 270311. CMP 99:06
 [LP]
 Q. Lin and N.C. Phillips, Ordered Ktheory for algebras of minimal homeomorphisms, Advances in Operator Algebras and Operator Theory, Contem. Math. 228 (1998), 289314.
 [Pi]
 M. Pimsner, Embedding some transformation group Calgebras into AF algebras, Ergod. Th. Dynam. Sys. 3 (1983), 613  626. MR 86d:46054
 [PV]
 M. Pimsner and D. Voiculescu, Exact sequences for Kgroups and Extgroups of certain crossed products of , 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 479071901
Address at time of publication:
Department of Mathematics, University of CaliforniaBerkeley, Berkeley, California 94720
Email:
nbrown@math.purdue.edu
DOI:
http://dx.doi.org/10.1090/S0002993900053296
PII:
S 00029939(00)053296
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
