Reconstructing directed graphs from generalized gauge actions on their Toeplitz algebras

Title: Reconstructing directed graphs from generalized gauge actions on their Toeplitz algebras
Creator: Brownlowe, Nathan; Laca, Marcelo; Robertson, Dave; Sims, Aidan
Relation: Proceedings of the Royal Society of Edinburgh Section A: Mathematics Vol. 150, Issue 5, p. 2632-2641
Publisher Link: http://dx.doi.org/10.1017/prm.2019.36
Publisher: The R S E Scotland Foundation
Resource Type: journal article
Date: 2020
Description: 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.
Subject: Graph C∗-algebra; Toeplitz algebra; KMS state
Identifier: http://hdl.handle.net/1959.13/1462124
Identifier: uon:46389
Identifier: ISSN:0308-2105
Language: eng
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