Reconstructing directed graphs from generalized gauge actions on their Toeplitz algebras

Authors

Nathan D. Brownlowe, University of SydneyFollow
Marcelo Laca, University of Victoria, CanadaFollow
David I. Robertson, University of NewcastleFollow
Aidan Sims, University of WollongongFollow

RIS ID

136579

Publication Details

Brownlowe, N., Laca, M., Robertson, D. & Sims, A. (2019). Reconstructing directed graphs from generalized gauge actions on their Toeplitz algebras. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, Online First 1-10.

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 to recover E from its Toeplitz algebra and gauge action alone.

Grant Number

ARC/DP180100595