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

 

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
Published electronically: January 17, 2006
MathSciNet review: 2215117
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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.


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Additional Information

Kin-Wai Tsang
Affiliation: Department of Mathematics, University of Toronto, 100 St. George Street, Tor- onto, 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
Published electronically: January 17, 2006
Communicated by: David R. Larson
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.