Graphs and CCR algebras

  title={Graphs and CCR algebras},
  author={Ilijas Farah},
  journal={arXiv: Operator Algebras},
  • 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. 
A simple C*-algebra with finite nuclear dimension which is not Z-stable
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
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
  • I. Farah
  • Mathematics
    Springer 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
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
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
  • A. Vaccaro
  • Mathematics
    Journal of Functional Analysis
  • 2018
The Calkin algebra is $\aleph_1$-universal
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
Evaluating the Magnetorotational Instability's Dependence on Numerical Algorithms and Resolution
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


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
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
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
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.
  • C. Akemann, N. Weaver
  • Mathematics, Medicine
    Proceedings 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
Nonseparable UHF algebras I: Dixmier’s problem, preprint
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
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
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)