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Reconstructing directed graphs from generalized gauge actions on their Toeplitz algebras

Journal Article


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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.

UOW Authors


  •   Brownlowe, Nathan D. (external author)
  •   Laca, Marcelo (external author)
  •   Robertson, Dave I. (external author)
  •   Sims, Aidan

Publication Date


  • 2019

Citation


  • 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.

Scopus Eid


  • 2-s2.0-85067338043

Ro Full-text Url


  • https://ro.uow.edu.au/cgi/viewcontent.cgi?article=4288&context=eispapers1

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers1/3267

Number Of Pages


  • 9

Start Page


  • 1

End Page


  • 10

Volume


  • Online First

Place Of Publication


  • United Kingdom

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.

UOW Authors


  •   Brownlowe, Nathan D. (external author)
  •   Laca, Marcelo (external author)
  •   Robertson, Dave I. (external author)
  •   Sims, Aidan

Publication Date


  • 2019

Citation


  • 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.

Scopus Eid


  • 2-s2.0-85067338043

Ro Full-text Url


  • https://ro.uow.edu.au/cgi/viewcontent.cgi?article=4288&context=eispapers1

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers1/3267

Number Of Pages


  • 9

Start Page


  • 1

End Page


  • 10

Volume


  • Online First

Place Of Publication


  • United Kingdom