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Reconstructing directed graphs from generalized gauge actions on their Toeplitz algebras
Published online by Cambridge University Press: 13 June 2019
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.
MSC classification
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 150 , Issue 5 , October 2020 , pp. 2632 - 2641
- Copyright
- Copyright © Royal Society of Edinburgh 2019
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