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

DOI:
https://doi.org/10.1090/S0002-9939-06-08215-3

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:
https://doi.org/10.1090/S0002-9939-06-08215-3

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.