# 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…

## 4 Citations

### C*-dynamical invariants and Toeplitz algebras of graphs

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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…

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. 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

- MathematicsCompositio Mathematica
- 2020

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

- Computer ScienceProceedings of the American Mathematical Society, Series B
- 2022

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.

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