Inverse Semigroups and Locally Compact Groupoids

1999 ◽  
pp. 21-84
Author(s):  
Alan L. T. Paterson
Keyword(s):  
Inverse Semigroups ◽  
Locally Compact

scholarly journals Embedding inverse semigroups of homeomorphisms on closed subsets

1977 ◽  
Vol 18 (2) ◽  
pp. 199-207 ◽  
Author(s):  
Bridget Bos Baird
Keyword(s):  
Topological Space ◽  
Inverse Semigroup ◽  
Inverse Semigroups ◽  
Topological Spaces ◽  
Locally Compact ◽  
Compact Metric Space ◽  
Countable Space ◽  
The One ◽  
One Point Compactification ◽  
First Countable Space

All topological spaces here are assumed to be T2. The collection F(Y)of all homeomorphisms whose domains and ranges are closed subsets of a topological space Y is an inverse semigroup under the operation of composition. We are interested in the general problem of getting some information about the subsemigroups of F(Y) whenever Y is a compact metric space. Here, we specifically look at the problem of determining those spaces X with the property that F(X) is isomorphic to a subsemigroup of F(Y). The main result states that if X is any first countable space with an uncountable number of points, then the semigroup F(X) can be embedded into the semigroup F(Y) if and only if either X is compact and Y contains a copy of X, or X is noncompact and locally compact and Y contains a copy of the one-point compactification of X.

scholarly journals An algebraic characterisation of ample type I groupoids

2021 ◽  
Author(s):  
Gabriel Favre ◽  
Sven Raum
Keyword(s):  
Inverse Semigroup ◽  
Inverse Semigroups ◽  
Type I ◽  
Locally Compact

AbstractWe give algebraic characterisations of the type I and CCR properties for locally compact second countable, ample Hausdorff groupoids in terms of subquotients of its Boolean inverse semigroup of compact open local bisections. It yields in turn algebraic characterisations of both properties for inverse semigroups with meets in terms of subquotients of their Booleanisation.

Locally compact bisimple inverse semigroups

1981 ◽  
Vol 22 (1) ◽  
pp. 387-389 ◽  
Author(s):  
Kadir R. Ahre
Keyword(s):  
Inverse Semigroups ◽  
Locally Compact

ON A GROUPOID CONSTRUCTION FOR ACTIONS OF CERTAIN INVERSE SEMIGROUPS

1994 ◽  
Vol 05 (03) ◽  
pp. 349-372 ◽  
Author(s):  
ALEXANDRU NICA
Keyword(s):  
Inverse Semigroup ◽  
Compact Space ◽  
Transformation Group ◽  
Algebraic Theory ◽  
Inverse Semigroups ◽  
Discrete Groups ◽  
Crossed Products ◽  
Locally Compact ◽  
Locally Compact Space ◽  
The One

We consider a version of the notion of F-inverse semigroup (studied in the algebraic theory of inverse semigroups). We point out that an action of such an inverse semigroup on a locally compact space has associated a natural groupoid construction, very similar to the one of a transformation group. We discuss examples related to Toeplitz algebras on subsemigroups of discrete groups, to Cuntz-Krieger algebras, and to crossed-products by partial automorphisms in the sense of Exel.

scholarly journals Amenable actions of inverse semigroups

2015 ◽  
Vol 37 (2) ◽  
pp. 481-489 ◽  
Author(s):  
RUY EXEL ◽  
CHARLES STARLING
Keyword(s):  
Inverse Semigroup ◽  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Inverse Semigroups ◽  
Locally Compact ◽  
Locally Compact Hausdorff Space

We say that an action of a countable discrete inverse semigroup on a locally compact Hausdorff space is amenable if its groupoid of germs is amenable in the sense of Anantharaman-Delaroche and Renault. We then show that for a given inverse semigroup ${\mathcal{S}}$, the action of ${\mathcal{S}}$ on its spectrum is amenable if and only if every action of ${\mathcal{S}}$ is amenable.

Sign in / Sign up

Export Citation Format

Share Document