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The groupoid algebra of an eigenvalue pattern
Author:
Kin-Wai Tsang
Journal:
Proc. Amer. Math. Soc. 134 (2006), 1899-1908
MSC (2000):
Primary 46L05; Secondary 46L35
Posted:
January 17, 2006
MathSciNet review:
2215117
Full-text PDF Free Access
Abstract |
References |
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Abstract: The eigenvalue pattern of a *-homomorphism between two matrix algebras over commutative C -algebras is a generalization of the Gelfand map in the commutative case. We give a systematic formulation of abstract eigenvalue pattern and extend the classical results by using a technique involving the groupoid algebras of eigenvalue patterns. In the case with matrix algebras over the one-dimensional circle, we characterize all the *-homomorphisms up to unitary equivalence by their eigenvalue patterns. Moreover, this technique has an application to recent classification theorems of C -algebras proved by the present author.
References
- [Br]
O. Bratteli, Inductive limits of finite dimensional C
 -algebras, Trans. Amer. Math. Soc. 171 (1972), 195-234. MR 0312282 (47:844)
- [EHS]
E. Effros, D. E. Handelman and C. L. Shen, Dimension groups and their affine representations, Amer. J. Math. 102 (1980), 385-407. MR 0564479 (83g:46061)
- [Ell1]
G. A. Elliott, On the classification of C
 -algebras of real rank zero, J. Reine Angew. Math. 443 (1993), 179-219. MR 1241132 (94i:46074)
- [Ell2]
G. A. Elliott, An invariant for simple C
 -algebras. Invited Papers/Articles sollicités, Canadian Mathematical Society 1945-1995, Volume 3 (eds. J. B. Carrell and R. Murty), Canadian Mathematical Society, Ottawa, 1996, 61-90. MR 1661611 (2000b:46095)
- [EV]
G. A. Elliott and J. Villadsen, Perforated K
 -groups. Canad. J. Math. 52 (2000), 1164-1191. MR 1794301 (2002j:46088)
- [Eva]
D. Evans, Quasiproduct states on C
 -algebras. Operator algebras and their connections with topology and ergodic theory (Busteni, 1983), 129-151, Lecture Notes in Math., 1132, Springer-Verlag, Berlin, 1985. MR 0799567 (87e:46079)
- [Go]
G. Gong, On the Classification of Simple Inductive Limit C
 -Algebras, I: The Reduction Theorem, Documenta Math. 7 (2002), 255-461 MR 2014489
- [Ra]
S. Razak, On the classification of simple stably projectionles C
 -algebras, Canad. J. Math. 54 (2002), 138-224. MR 1880962 (2003h:46091)
- [Re]
J. Renault, A groupoid approach to C
 -algebras, Lecture Notes in Mathematics 793, Springer-Verlag, Berlin, 1980. MR 0584266 (82h:46075)
- [Ts1]
K. W. Tsang, A classification of certian simple stably projectionless C
 -algebras, submitted.
- [Ts2]
K. W. Tsang, On the positive tracial cones of simple stably projectionless C
 -algebras, to appear in J. Funct. Anal..
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Additional Information
Kin-Wai Tsang
Affiliation:
Department of Mathematics, University of Toronto, 100 St. George Street, Toronto, Ontario, Canada M5S 3G3
Address at time of publication:
Department of Mathematics, D3-2/F-09, The Hong Kong Institute of Education, 10 Lo Ping Road, Tai Po, Hong Kong
Email:
tsang@math.toronto.edu, kwtsang@ied.edu.hk
DOI:
http://dx.doi.org/10.1090/S0002-9939-06-08215-3
PII:
S 0002-9939(06)08215-3
Keywords:
Groupoid algebra,
path space,
singular eigenvalue pattern,
Gelfand map
Received by editor(s):
June 1, 2003
Received by editor(s) in revised form:
February 1, 2005
Posted:
January 17, 2006
Communicated by:
David R. Larson
Article copyright:
© Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain after
28 years from publication.
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