کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4657895 1633071 2016 21 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Topological graph inverse semigroups
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات هندسه و توپولوژی
پیش نمایش صفحه اول مقاله
Topological graph inverse semigroups
چکیده انگلیسی

To every directed graph E one can associate a graph inverse semigroup  G(E)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⁎C⁎-algebras. We investigate topologies that turn G(E)G(E) into a topological semigroup. For instance, we show that in any such topology that is Hausdorff, G(E)∖{0}G(E)∖{0} must be discrete for any directed graph E  . On the other hand, G(E)G(E) need not be discrete in a Hausdorff semigroup topology, and for certain graphs E  , G(E)G(E) admits a T1T1 semigroup topology in which G(E)∖{0}G(E)∖{0} is not discrete. We also describe, in various situations, the algebraic structure and possible cardinality of the closure of G(E)G(E) in larger topological semigroups.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 208, 1 August 2016, Pages 106–126
نویسندگان
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