Finite dimensional representations of the soft torus

Eilers, Søren; Exel, Ruy

doi:10.1090/S0002-9939-01-06150-0

Finite dimensional representations of the soft torus
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by Søren Eilers and Ruy Exel PDF

Proc. Amer. Math. Soc. 130 (2002), 727-731 Request permission

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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