# Graphs and CCR algebras

@article{Farah2009GraphsAC, title={Graphs and CCR algebras}, author={Ilijas Farah}, journal={arXiv: Operator Algebras}, year={2009} }

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.

## 11 Citations

A simple C*-algebra with finite nuclear dimension which is not Z-stable

- Mathematics
- 2013

We construct a simple C*-algebra with nuclear dimension zero that is not isomorphic to its tensor product with the Jiang-Su algebra Z, and a hyperfinite II_1 factor not isomorphic to its tensor…

Logic and operator algebras

- Mathematics
- 2014

The most recent wave of applications of logic to operator algebras is a young and rapidly developing field. This is a snapshot of the current state of the art.

Constructions of Nonseparable C∗-algebras, I: Graph CCR Algebras

- MathematicsSpringer Monographs in Mathematics
- 2019

In this chapter, infinitary combinatorics is applied to study graph CCR algebras. These “twisted” reduced group C∗-algebras associated with a Boolean group and a cocycle given by a graph are AF…

Nonseparable UHF algebras II: Classification

- Mathematics
- 2013

For every uncountable cardinal $\kappa$ there are $2^\kappa$ nonisomorphic simple AF algebras of density character $\kappa$ and $2^\kappa$ nonisomorphic hyperfinite II$_1$ factors of density…

The Calkin algebra is ℵ1-universal

- Mathematics
- 2020

We discuss the existence of (injectively) universal C*-algebras and prove that all C*-algebras of density character ℵ1 embed into the Calkin algebra, Q(H). Together with other results, this shows…

Trace spaces of counterexamples to Naimark's problem

- MathematicsJournal of Functional Analysis
- 2018

The Calkin algebra is $\aleph_1$-universal

- Mathematics
- 2017

We discuss the existence of (injectively) universal C*-algebras and prove that all C*-algebras of density character $\aleph_1$ embed into the Calkin algebra, $Q(H)$. Together with other results, this…

Corrigendum to “Trace spaces of counterexamples to Naimark's problem” [J. Funct. Anal. 275 (10) (2018) 2794–2816]

- Mathematics
- 2020

Evaluating the Magnetorotational Instability's Dependence on Numerical Algorithms and Resolution

- Physics
- 2010

We have studied saturated, MRI-driven turbulence using three-dimensional, isothermal simulations with resolutions that extend from 64 to 192 zones in each direction. The simulations were performed…

## References

SHOWING 1-10 OF 17 REFERENCES

Set Theory and C*-Algebras

- Computer Science, MathematicsBulletin 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

- Mathematics
- 1972

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

- MathematicsCanadian Mathematical Bulletin
- 2003

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 ${{C}^{*}}$…

Consistency of a counterexample to Naimark's problem.

- Mathematics, MedicineProceedings of the National Academy of Sciences of the United States of America
- 2004

It is proved that the statement "there exists a counterexample to Naimark's problem which is generated by aleph (1) elements" is undecidable in standard set theory.

Nonseparable UHF algebras I: Dixmier’s problem, preprint

- 2009

There are three natural ways to define UHF (uniformly hyperfinite) C*-algebras, and all three definitions are equivalent for separable algebras. In 1967 Dixmier asked whether the three definitions…

Operator Algebras

- 1998

p. 2 I.1.1.4: The Riesz-Fischer Theorem is often stated this way today, but neither Riesz nor Fischer (who worked independently) phrased it in terms of completeness of the orthogonal system {e}. If…

SET THEORY AND OPERATOR ALGEBRAS

- Mathematics
- 2010

These notes are based on the six-hour Appalachian Set Theory workshop given by Ilijas Farah on February 9th, 2008 at Carnegie Mellon University. The first half of the workshop (Sections 1–4)…