# Graphs and CCR algebras

@article{Farah2009GraphsAC,
title={Graphs and CCR algebras},
author={Ilijas Farah},
journal={arXiv: Operator Algebras},
year={2009}
}
• I. Farah
• Published 27 August 2009
• Mathematics
• arXiv: Operator Algebras
I introduce yet another way to associate a C*-algebra to a graph and construct a simple nuclear C*-algebra that has irreducible representations both on a separable and a nonseparable Hilbert space.
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## References

SHOWING 1-10 OF 17 REFERENCES
Set Theory and C*-Algebras
• N. Weaver
• Computer Science, Mathematics
Bulletin of Symbolic Logic
• 2007
The use of extra-set-theoretic hypotheses, mainly the continuum hypothesis, in the C*-algebra literature are surveyed, and the Calkin algebra emerges as a basic object of interest.
Classification of Nuclear C*-Algebras. Entropy in Operator Algebras
• Mathematics
• 2001
I. Classification of Nuclear, Simple C*-algebras.- II. A Survey of Noncommutative Dynamical Entropy.
On factor representations and theC*-algebra of canonical commutation relations
A newC*-algebra,A, for canonical commutation relations, both in the case of finite and infinite number of degrees of freedom, is defined. It has the property that to each, not necessarily continuous,
Homegeneity of the pure state space for separable C*-algebras
• Mathematics
• 2001
We prove that the pure state space is homogeneous under the action of the automorphism group (or a certain smaller group of approximately inner automorphisms) for a fairly large class of simple
Homogeneity of the Pure State Space of a Separable ${{C}^{*}}$ -Algebra
• Mathematics
Abstract We prove that the pure state space is homogeneous under the action of the automorphism group (or the subgroup of asymptotically inner automorphisms) for all the separable simple ${{C}^{*}}$