Reconstructing directed graphs from generalised gauge actions on their Toeplitz algebras
Operator Algebras
2018-12-24 v1
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 generalised 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.
Cite
@article{arxiv.1812.08903,
title = {Reconstructing directed graphs from generalised gauge actions on their Toeplitz algebras},
author = {Nathan Brownlowe and Marcelo Laca and David Robertson and Aidan Sims},
journal= {arXiv preprint arXiv:1812.08903},
year = {2018}
}
Comments
9 pages; pictures drawn using TiKZ