Related papers: Boolean inverse semigroups and their type monoids
We define and study the notion of a crossed module over an inverse semigroup and the corresponding $4$-term exact sequences, called crossed module extensions. For a crossed module $A$ over an $F$-inverse monoid $T$, we show that equivalence…
We develop a technique to show the Morita equivalence of certain subrings of a ring with local units. We then apply this technique to develop conditions that are sufficient to show the Morita equivalence of subalgebras induced by partial…
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…
Let G be a finite group that acts on an abelian monoid A. If f: A -> G is a map so that f(a f(a)(b)) = f(a)f(b), for all a, b in A, then the submonoid S = {(a, f(a)) | a in A} of the associated semidirect product of A and G is said to be a…
We give a thorough structural analysis of the principal one-sided ideals of arbitrary semigroups, and then apply this to full transformation semigroups and symmetric inverse monoids. One-sided ideals of these semigroups naturally occur as…
There are well known relations between braid groups and symmetric groups, between Artin-Briskorn braid groups and Coxeter groups. Inverse braid monoid the same way is related to the inverse symmetric monoid. In the paper we show that…
For a topological monoid S the dual inverse monoid is the topological monoid of all identity preserving homomorphisms from S to the circle with attached zero. A topological monoid S is defined to be reflexive if the canonical homomorphism…
Some sorts of generalized morphisms are defined from very basic mathematical objects such as sets, functions, and partial functions. A wide range of mathematical notions such as continuous functions between topological spaces, ring…
To a Boolean inverse monoid $S$ we associate a universal C*-algebra $C_B^*(S)$ and show that it is equal to Exel's tight C*-algebra of $S$. We then show that any invariant mean on $S$ (in the sense of Kudryavtseva, Lawson, Lenz and Resende)…
A simple observation, showing that every groupoid becomes an inverse semigroup after adding one element. In such inverse semigroups all idempotents are mutually orthogonal. This fact implies that every C*-algebra of a discrete groupoid is a…
We study locally closed transformation monoids which contain the automorphism group of the random graph. We show that such a transformation monoid is locally generated by the permutations in the monoid, or contains a constant operation, or…
We generalise the Milnor-Schwarz lemma to inverse monoids acting on presheaves of geodesic metric spaces. We provide two proofs of this fact: one only uses elementary techniques, inspired by the arguments for group actions on metric spaces;…
The purpose of this paper is to study the generalization of inverse semigroups (without order). An ordered semigroup S is called an inverse ordered semigroup if for every a 2 S, any two inverses of a are H-related. We prove that an ordered…
In this paper we provide an overview of the class of inverse semigroups $S$ such that every congruence on $S$ relates at least one idempotent to a non-idempotent; such inverse semigroups are called $E$-disjunctive. This overview includes…
We develop a structural theory of chirality for inverse semigroups and show how it propagates canonically to \'{e}tale groupoids and twisted groupoid $C^*$-algebras. Starting from inverse semigroup data equipped with admissible twist…
We investigate Cayley graphs of finite semigroups and monoids. First, we look at semigroup digraphs, i.e., directed Cayley graphs of semigroups, and give a Sabidussi-type characterization in the case of monoids. We then correct a proof of…
A theory of monoids in the category of bicomodules of a coalgebra $C$ or $C$-rings is developed. This can be viewed as a dual version of the coring theory. The notion of a matrix ring context consisting of two bicomodules and two maps is…
We show that each connected group scheme of finite type over an arbitrary ground field is isomorphic to the component of the identity inside the automorphism group scheme of some projective, geometrically integral scheme. The main…
In this paper subcentral (resp., central) idempotent series and composition subcentral (resp., central) idempotent series in an inverse semigroup are introduced and investigated. It is shown that if $S=EG$ is a factorizable inverse monoids…
Let S be a compact oriented surface. A homology cobordism of S is a cobordism C between two copies of S, such that both the "top" inclusion and the "bottom" inclusion of S in C induce isomorphisms in homology. Homology cobordisms of S form…