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The groupoid algebra of an eigenvalue pattern

Author(s): Kin-Wai Tsang
Journal: Proc. Amer. Math. Soc. 134 (2006), 1899-1908.
MSC (2000): Primary 46L05; Secondary 46L35
Posted: January 17, 2006
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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, 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: 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
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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