Topological graph inverse semigroups

Z. Mesyan, J. D. Mitchell, M. Morayne, Y. H. Péresse

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

Abstract

To every directed graph E one can associate a graph inverse semigroup G(E), where elements roughly correspond to possible paths in E . These semigroups generalize polycyclic monoids, and they arise in the study of Leavitt path algebras, Cohn path algebras, graph C⁎C⁎-algebras, and Toeplitz C-algebras. We investigate topologies that turn G(E) into a topological semigroup. For instance, we show that in any such topology that is Hausdorff, G(E)∖{0} must be discrete for any directed graph E . On the other hand, G(E) need not be discrete in a Hausdorff semigroup topology, and for certain graphs E , G(E) admits a T1 semigroup topology in which G(E)∖{0} is not discrete. We also describe, in various situations, the algebraic structure and possible cardinality of the closure of G(E) in larger topological semigroups.
Original languageEnglish
Pages (from-to)106-126
Number of pages21
JournalTopology and Its Applications
Volume208
Early online date24 May 2016
DOIs
Publication statusPublished - 1 Aug 2016

Keywords

  • Graph inverse semigroup
  • Polycyclic monoid
  • Topological semigroup

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