Topological graph inverse semigroups
Date
01/08/2016Metadata
Show full item recordAbstract
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.
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
Publication
Topology and Its Applications
Status
Peer reviewed
ISSN
0166-8641Type
Journal article
Description
Michał Morayne was partially supported by NCN grant DEC-2011/01/B/ST1/01439 while this work was performed.Collections
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