Related papers: Filtering germs: Groupoids associated to inverse s…
Given a graded ample Hausdorff groupoid, we realise its graded Steinberg algebra as a partial skew inverse semigroup ring. We use this to show that for a partial action of a discrete group on a locally compact Hausdorff topological space,…
A groupoid is a small category in which each morphism has an inverse. A topological groupoid is a groupoid in which both sets of objects and morphisms have topologies such that all groupoid structure maps are continuous. The notion of…
In this paper, we define a new structure analogous to group, called partial group. This structure concerns the partial stability by the composition inner law. We generalize the three isomorphism theorems for groups to partial groups.
As an appropriate generalisation of the features of the classical (Schein) theory of representations of inverse semigroups in $\mathscr{I}_{X}$, a theory of representations of inverse semigroups by homomorphisms into complete atomistic…
A completely inverse $AG^{**}$-groupoid is a groupoid satisfying the identities $(xy)z=(zy)x$, $x(yz)=y(xz)$ and $xx^{-1}=x^{-1}x$, where $x^{-1}$ is a unique inverse of $x$, that is, $x=(xx^{-1})x$ and $x^{-1}=(x^{-1}x)x^{-1}$. First we…
A semigroup together with compatible partial order is called an odered semigroup. In this paper we discuss the ordered matrix semigroups.
In this paper we compute the rank and exhibit a presentation for the monoids of all $P$-stable and $P$-order preserving partial permutations on a finite set $\Omega$, with $P$ an ordered uniform partition of $\Omega$. These (inverse)…
We develop the theory of distributive inverse semigroups as the analogue of distributive lattices without top element and prove that they are in a duality with those etale groupoids having a spectral space of identities, where our spectral…
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…
In an earlier work, the author observed that Boolean inverse semi-groups, with semigroup homomorphisms preserving finite orthogonal joins, form a congruence-permutable variety of algebras, called biases. We give a full description of…
Let a finite group $G$ act on the complex plane $({\Bbb C}^2, 0)$. We consider multi-index filtrations on the spaces of germs of holomorphic functions of two variables equivariant with respect to 1-dimensional representations of the group…
We continue algebraization of the set of ultrafilters on a metric spaces initiated in [6]. In particular, we define and study metric counterparts of prime, strongly prime and right cancellable ultrafilters from the Stone-$\check{C}$ech…
The symmetric inverse monoid $I_X$ on a set $X$ consists of all bijective functions whose domain and range are subsets of $X$ under the usual composition and inversion of partial functions. For an arbitrary infinite set $X$, we classify all…
We establish rigidity for partial transformation groupoids associated with algebraic actions of semigroups: If two such groupoids (satisfying appropriate conditions) are isomorphic, then the globalizations of the initial algebraic actions…
We provide a framework for studying concrete C*-algebras associated with algebraic actions of semigroups: Given such an action, we construct an inverse semigroup, and we introduce conditions for algebraic actions that characterize…
The semigroup $\mathbf{I}\mathbb{N}_{\infty}$ of all partial co-finite isometries of positive integers is studied. We describe Green's relations on the semigroup $\mathbf{I}\mathbb{N}_{\infty}$, its band and proved that…
We provide a necessary and sufficient condition to the existence of an ordered globalization of a partial ordered action of an ordered groupoid on a ring and we also present criteria to obtain uniqueness. Furthermore, we apply those results…
We show that the fundamental groups of any two closed irreducible non-geometric graph-manifolds are quasi-isometric. This answers a question of Kapovich and Leeb. We also classify the quasi-isometry types of fundamental groups of…
In this paper the concept of local embeddability into finite structures (being LEF) for the class of semigroups is expanded with investigations of non-LEF structures, a closely related generalising property of local wrapping of finite…
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…