dc.contributor.author | Mesyan, Zak | |
dc.contributor.author | Mitchell, J. D. | |
dc.contributor.author | Morayne, Michal | |
dc.contributor.author | Péresse, Y. H. | |
dc.date.accessioned | 2016-09-22T11:16:45Z | |
dc.date.available | 2016-09-22T11:16:45Z | |
dc.date.issued | 2016-08-01 | |
dc.identifier.citation | Mesyan , Z , Mitchell , J D , Morayne , M & Péresse , Y H 2016 , ' Topological Graph Inverse Semigroups ' , Topology and its Applications , vol. 208 , pp. 106-126 . https://doi.org/10.1016/j.topol.2016.05.012 | |
dc.identifier.issn | 0166-8641 | |
dc.identifier.other | ArXiv: http://arxiv.org/abs/1306.5388v2 | |
dc.identifier.uri | http://hdl.handle.net/2299/17248 | |
dc.description.abstract | 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. | en |
dc.format.extent | 21 | |
dc.format.extent | 258579 | |
dc.language.iso | eng | |
dc.relation.ispartof | Topology and its Applications | |
dc.subject | Topological Algebra | |
dc.subject | SEMIGROUPS | |
dc.subject | Abstract Algebra | |
dc.title | Topological Graph Inverse Semigroups | en |
dc.contributor.institution | School of Physics, Astronomy and Mathematics | |
dc.description.status | Peer reviewed | |
dc.date.embargoedUntil | 2017-05-24 | |
dc.identifier.url | http://arxiv.org/pdf/1306.5388v2.pdf | |
rioxxterms.versionofrecord | 10.1016/j.topol.2016.05.012 | |
rioxxterms.type | Journal Article/Review | |
herts.preservation.rarelyaccessed | true | |