Related papers: Primer on inverse semigroups I

We introduce the notion of wide representation of an inverse semigroup and prove that with a suitably defined topology there is a space of germs of such a representation which has the structure of an etale groupoid. This gives an elegant…

We describe the structure of finite Boolean inverse monoids and apply our results to the representation theory of finite inverse semigroups. We then generalize to semisimple Boolean inverse semigroups.

These are lecture notes for a one semester introductory course I gave at Indiana University. The goal was to make this exposition as clear and elementary as possible. A particular emphasis is given on examples involving SU(1,1). These notes…

This is a survey paper based on my talk at the Workshop on Orbifolds and String Theory, the goal of which was to explain the role of groupoids and their classifying spaces as a foundation for the theory of orbifolds.

We introduce locally involutive semigroups and embed them into the category of ordered groupoids. This embedding restricts to a correspondence between quasi-involutive semigroups and ordered groupoids with mediator, extending the classical…

This paper studies simplicity, primitivity and semiprimitivity of algebras associated to \'etale groupoids. Applications to inverse semigroup algebras are presented. The results also recover the semiprimitivity of Leavitt path algebras and…

This paper serves as an example to show the way we pass from semigroups to $\Gamma$-semigroups and to hypersemigroups.

We give an account of the theory of $E_0$-semigroups. We first focus on Arveson's contributions to the field and related results. Then we present the recent development of type II and type III $E_0$-semigroups. We also include a short note…

We present some of the group theoretic properties of reversing symmetry groups, and classify their structure in simple cases that occur frequently in several well-known groups of dynamical systems.

Congruences on a graph inverse semigroup were recently described in terms of the underline graph. Based on such descriptions, we show that the lattice of congruences on a graph inverse semigroup is upper semimodular but not lower…

First and second fundamental theorems are given for polynomial invariants of a class of pseudo-reflection groups (including the Weyl groups of type $B_n$), under the assumption that the order of the group is invertible in the base field.…

For a given inverse semigroup, one can associate an \'etale groupoid which is called the universal groupoid. Our motivation is studying the relation between inverse semigroups and associated \'etale groupoids. In this paper, we focus on…

The thesis is devoted to abstract, geometric and symmetric aspects of modern elementary particle theories. A new direction in constructing supersymmetric and superstring models based on consequent and strong consideration and inclusion of…

Various connections between the theory of permutation groups and the theory of topological groups are described. These connections are applied in permutation group theory and in the structure theory of topological groups. The first draft of…

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.

The matched pair theory (of groups) is studied for a class of quasigroups; namely, the $m$-inverse property loops. The theory is upgraded to the Hopf level, and the "$m$-invertible Hopf quasigroups" are introduced.

The area of inverse problems in mathematics is highly interdisciplinary. In various fields of science, engineering, medicine, and industry, there arises a need to reconstruct information about unknown entities that cannot be directly…

In this paper, we give a different proof of the fact that the $C^{*}$ algebra of the odd dimensional quantum spheres is a groupoid $C*}$ algebra. We use the theory of inverse semigroups to reconstruct the groupoid given by Sheu in [6].

Motivated by recent appearance of multivalued structures in categorification, tropical geometry and other areas, we study basic properties of abstract multisemigroups. We give many new and old examples and general constructions for…

The m-weak group inverse was recently studied in the literature. The purpose of this paper is to investigate new properties of this generalized inverse for ring elements. We introduce the m-weak group decomposition for a ring element and…