Related papers: Group-groupoids and monodromy groupoids
In this article, we introduce an interesting topology-like concept concerning groups (and with almost the same method it can be defined for other algebraic systems). Given an arbitrary group $G$, we define a {\em topo-system} on $G$ as a…
In this note for a topological group $G$, we introduce a bounded subset of $G$ and we find some relationships of this definition with other topological properties of $G$.
The aim of this paper is to present a simplified version of the notion of $\infty$-groupoid developed by Grothendieck in "Pursuing Stacks" and to introduce a definition of $\infty$-categories inspired by Grothendieck's approach.
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.
In this paper, Ramsey theory for discrete hypergroups is introduced with emphasis on polynomial hypergroups, discrete orbit hypergroups and hypergroup deformations of semigroups. In this context, new notions of Ramsey principle for…
We introduce and study the class of spherically ordered groups. The notions of spherically ordered groups and their spectra of spherical orderability are introduced. Values of these spectra are found for a series of natural groups.
In this paper, we mainly discuss some generalized metric properties and the character of the free paratopological groups, and extend several results valid for free topological groups to free paratopological groups.
Group Theory has become an invaluable tool in the physics community. Despite numerous introductory books, the subject remains challenging for beginners. Mathematica has emerged as a popular tool for research and education, offering various…
The paper is a short survey of recent developments in the area of first order descriptions of linear groups. It is aimed to illuminate the known results and to pose the new problems relevant to logical characterizations of Chevalley groups…
We describe sofic groupoids in elementary terms and prove several permanence properties for sofcity. We show that sofcity can be determined in terms of the full group alone, answering a question by Conley, Kechris and Tucker-Drob.
We investigate which aspects of recent developments on Galois corings and comodules admit a formulation in terms of comonads. This approach hopefully will permit of focusing in what is specific in each particular future situation, having…
The representation theory for categorical groups is constructed. Each categorical group determines a monoidal bicategory of representations. Typically, these categories contain representations which are indecomposable but not irreducible. A…
Necessary and sufficient conditions are given for the endomorphism monoid of a profinite semigroup to be profinite. A similar result is established for the automorphism group.
By extending type theory with a universe of definitionally associative and unital polynomial monads, we show how to arrive at a definition of opetopic type which is able to encode a number of fully coherent algebraic structures. In…
This paper surveys some results and methods in topological transformation groups.
The article presents a complete classification of $n$-valued monoids and groups of order 3. Important corollaries of this result are discussed.
We provide a unified treatment of several results concerning full groups of ample groupoids and paradoxical decompositions attached to them. This includes a criterion for the full group of an ample groupoid being amenable as well as…
In analogy with the classical theory of topological groups, for finitely complete categories enriched with Grothendieck topologies, we provide the concepts of localized G-topological space, initial Grothendieck topologies and continuous…
We discuss the history of the monodromy theorem, starting from Weierstra\ss, and the concept of monodromy group. From this viewpoint we compare then the Weierstra\ss , the Legendre and other normal forms for elliptic curves, explaining…
In a previous article, an `invariant method' to calculate monomial integrals over the U(n) group was introduced. In this paper, we study the more traditional group-theoretical method, and compare its strengths and weaknesses with those of…