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

 

Finite dimensional representations of the soft torus


Authors: Søren Eilers and Ruy Exel
Journal: Proc. Amer. Math. Soc. 130 (2002), 727-731
MSC (2000): Primary 46L05; Secondary 46L65, 46L85, 47B20
Published electronically: June 21, 2001
MathSciNet review: 1866027
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Abstract | References | Similar Articles | Additional Information

Abstract:

The soft tori constitute a continuous deformation, in a very precise sense, from the commutative $C^*$-algebra $C(\mathbb{T} ^2)$ to the highly non-commutative $C^*$-algebra $C^*(\mathbb{F} _2)$. Since both of these $C^*$-algebras are known to have a separating family of finite dimensional representations, it is natural to ask whether that is also the case for the soft tori. We show that this is in fact the case.


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Additional Information

Søren Eilers
Affiliation: Matematisk Afdeling, Københavns Universitet, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark
Email: eilers@math.ku.dk

Ruy Exel
Affiliation: Departamento de Matemática, Universidade Federal de Santa Catarina, 88040-900 Florianópolis SC, Brazil
Email: exel@mtm.ufsc.br

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06150-0
PII: S 0002-9939(01)06150-0
Received by editor(s): November 19, 1998
Received by editor(s) in revised form: August 28, 2000
Published electronically: June 21, 2001
Additional Notes: This work was partially supported by the Carlsberg Foundation
Communicated by: David R. Larson
Article copyright: © Copyright 2001 American Mathematical Society