Related papers: A Generalisation of the Munn Semigroup
The symmetric inverse semigroup $I(X)$ on a set $X$ is the collection of all partial bijections between subsets of $X$ with composition as the algebraic operation. We study a minimal Hausdorff inverse semigroup topologies on $I(X)$. When…
We call a restriction semigroup almost perfect if it is proper and its least monoid congruence is perfect. We show that any such semigroup is isomorphic to a `$W$-product' $W(T,Y)$, where $T$ is a monoid, $Y$ is a semilattice and there is a…
The article $-$ part of a larger thesis which aims to give a detailed description of the generalisation to the category of groups with operators of the classical theory of semisimplicity for modules $-$ presents a straightforward…
In this paper we construct a generalization of the classical Steinberg section for the quotient map of a semisimple group with respect to the conjugation action. We then give various applications of our construction including the…
By a "Boolean inverse semigroup" we mean an inverse semigroup whose semilattice of idempotents is a Boolean algebra. We study representations of a given inverse semigroup S in a Boolean inverse semigroup which are "tight" in a certain well…
We introduce the concept of a non-associative (i.e. non-necessarily associtive) inverse semialgebra over a field, the Lie version of which is inspired by the set of all partially defined derivations of a non-associative algebra, whereas the…
Given a monoid $S$ with $E$ any non-empty subset of its idempotents, we present a novel one-sided version of idempotent completion we call left $E$-completion. In general, the construction yields a one-sided variant of a small category…
We introduce partial semigroupoid actions on sets and demonstrate that each such action admits universal globalization. Our construction extends the universal globalization for partial category actions given by P. Nystedt (Lundstr\"om) and…
In this paper we discuss some enlargements of the category of sets with semigroup actions and equivariant functions. We show that these enlarged categories possess two idempotent endofunctors. In the case of groups these enlarged categories…
We establish representation types (finite, tame or wild) of finite dimensional Munn algebras with semisimple bases. As an application, we establish representation types of finite 0-simple semigroups and their mutually annihilating unions.
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…
We have shown recently that, given a metric space $X$, the coarse equivalence classes of metrics on the two copies of $X$ form an inverse semigroup $M(X)$. Here we give several descriptions of the set $E(M(X))$ of idempotents of this…
We construct the non-linear realisation of the semi-direct product of E(11) and its first fundamental representation at lowest order and appropriate to spacetime dimensions four to seven. This leads to a non-linear realisation of the…
We describe the structure of $E-$dense acts over $E-$dense semigroups in an analogous way to that for inverse semigroup acts over inverse semigroups. This is based, to a large extent, on the work of Schein on representations of inverse…
We present a construction for the holomorph of an inverse semigroup, derived from the cartesian closed structure of the category of ordered groupoids. We compare the holomorph with the monoid of mappings that preserve the ternary heap…
We give a simple construction involving partial actions which permits us to obtain an easy proof of a weakened version of L. O'Carroll's theorem on idempotent pure extensions of inverse semigroups.
Graph inverse semigroups generalize the polycyclic inverse monoids and play an important role in the theory of C*-algebras. This paper has two main goals: first, to provide an abstract characterization of graph inverse semigroups; and…
An element e of an ordered semigroup $(S,\cdot,\leq)$ is called an ordered idempotent if $e\leq e^2$. We call an ordered semigroup $S$ idempotent ordered semigroup if every element of $S$ is an ordered idempotent. Every idempotent semigroup…
We initiate the study of group actions on (possibly infinite) semimatroids and geometric semilattices. To every such action is naturally associated an orbit-counting function, a two-variable "Tutte" polynomial and a poset which, in the…
We unify various \'etale groupoid reconstruction theorems such as: 1) Kumjian-Renault's reconstruction from a groupoid C*-algebra. 2) Exel's reconstruction from an ample inverse semigroup. 3) Steinberg's reconstruction from a groupoid ring.…