Research output: Research - peer-review › Article

- Topological graph inverse semigroups AAM
Accepted author manuscript, 252 KB, PDF-document

- http://arxiv.org/pdf/1306.5388v2.pdf
Accepted author manuscript

Original language | English |
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Number of pages | 21 |

Pages (from-to) | 106-126 |

Journal | Topology and its Applications |

Journal publication date | 1 Aug 2016 |

Early online date | 24 May 2016 |

DOIs | |

State | Published - 1 Aug 2016 |

To every directed graph $E$ one can associate a \emph{graph inverse semigroup} $G(E)$, where elements roughly correspond to possible paths in $E$. These semigroups generalize polycylic monoids, and they arise in the study of Leavitt path algebras, Cohn path algebras, Cuntz-Krieger $C^*$-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, $G(E)\setminus \{0\}$ 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 $T_1$ semigroup topology in which $G(E)\setminus \{0\}$ 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.

ID: 10300989