Reconstructing directed graphs from generalized gauge actions on their Toeplitz algebras

@article{Brownlowe2018ReconstructingDG,
  title={Reconstructing directed graphs from generalized gauge actions on their Toeplitz algebras},
  author={Nathan Brownlowe and Marcelo Laca and David Robertson and Aidan Sims},
  journal={Proceedings of the Royal Society of Edinburgh: Section A Mathematics},
  year={2018},
  volume={150},
  pages={2632 - 2641}
}
Abstract We show how to reconstruct a finite directed graph E from its Toeplitz algebra, its gauge action, and the canonical finite-dimensional abelian subalgebra generated by the vertex projections. We also show that if E has no sinks, then we can recover E from its Toeplitz algebra and the generalized gauge action that has, for each vertex, an independent copy of the circle acting on the generators corresponding to edges emanating from that vertex. We show by example that it is not possible… 

C*-dynamical invariants and Toeplitz algebras of graphs

In recent joint work of the authors with Laca, we precisely formulated the notion of partition function in the context of C*-dynamical systems. Here, we compute the partition functions of

Reconstruction of topological graphs and their Hilbert bimodules

. We show that the Hilbert bimodule associated to a compact topological graph can be recovered from the C ∗ -algebraic triple consisting of the Toeplitz algebra of the graph, its gauge action and the

Classification of irreversible and reversible Pimsner operator algebras

Abstract Since their inception in the 1930s by von Neumann, operator algebras have been used to shed light on many mathematical theories. Classification results for self-adjoint and non-self-adjoint

Amplified graph C*-algebras II: Reconstruction

It is shown that the edges of the countable directed graph can be recovered from theinline-formula content-type "math/mathml", and that there are infinitely many edges from this content.

References

SHOWING 1-10 OF 19 REFERENCES

KMS states on the C*-algebras of reducible graphs

We consider the dynamics on the C*-algebras of finite graphs obtained by lifting the gauge action to an action of the real line. Enomoto, Fujii and Watatani proved that if the vertex matrix of the

Isomorphisms of algebras associated with directed graphs

Abstract.Given countable directed graphs G and G′, we show that the associated tensor algebras (G) and (G′) are isomorphic as Banach algebras if and only if the graphs G are G′ are isomorphic. For

The Toeplitz algebra of a Hilbert bimodule

Suppose a C*-algebra A acts by adjointable operators on a Hilbert A-module X. Pimsner constructed a C*-algebra O_X which includes, for particular choices of X, crossed products of A by Z, the Cuntz

On the classification of nonsimple graph C*-algebras

We prove that a graph C*-algebra with exactly one proper nontrivial ideal is classified up to stable isomorphism by its associated six-term exact sequence in K-theory. We prove that a similar

Amplified graph C*-algebras

We provide a complete invariant for graph C*-algebras which are amplified in the sense that whenever there is an edge between two vertices, there are infinitely many. The invariant used is the

KMS states on finite-graph C*-algebras

We study KMS states on finite-graph C*-algebras with sinks and sources. We compare finite-graph C*-algebras with C*-algebras associated with complex dynamical systems of rational functions. We show