Related papers: Algebraic properties of G-groupoids

The chapter provides an introduction to the basic concepts of Algebraic Topology with an emphasis on motivation from applications in the physical sciences. It finishes with a brief review of computational work in algebraic topology,…

In this paper we introduce elements of algebraic geometry over an arbitrary algebraic structure. We prove Unification Theorems which gather the description of coordinate algebras by several ways.

The construction of a C*-algebra of a differential groupoid is presented. It is shown that it defines a covariant functor from the category of differential groupoids in a sense of S. Zakrzewski to the category of C*-algebras.

The transformation properties of a Kalb-Ramond field are those of a gauge field; however, it is not clear which is the group structure these transformations are associated with. The purpose of this letter is to establish a basic framework…

We obtain a lifting property for finite quotients of algebraic groups, and applications to the structure of these groups.

A group, defined as set with associative multiplication and inverse, is a natural structure describing the symmetry of a space. The concept of group generalizes to group objects internal to other categories than sets. But there are yet more…

In this paper, we define the concept of the bi g-frame and then show some properties of the bi g-frame

Several results on presenting an affine algebraic group variety as a product of algebraic varieties are obtained.

A $\mathcal{C}$-set is a functor from the category $\mathcal{C}$ to the category of finite sets and functions. The category of $\mathcal{C}$-sets, $\mathcal{C} - \operatorname*{set}$, is defined as the category whose objects are…

In this paper the structure of the Cayley graphs and G-graphs of some gyro-groups are studied and some properties of them will be proved. Moreover we review some special gyro-groups including: gyro-commutative gyrogroups, dihedral…

The goal of this paper is to consider some relations between varieties of representations of groups and varieties of associative algebras. The main emphasis is put on the varieties of representations of groups induced by the varieties of…

The intention of this article is to make an attempt of classification of transitive Lie algebroids and on this basis to construct a classifying space. The realization of the intention allows to describe characteristic classes of transitive…

We report on recent progress concerning the relationship that exists between the algebraic structure of a finite group and certain features of its class-size prime graph.

In this paper, we establish the theory of nilpotent hypergroups and study some properties of nilpotent hypergroups and provided some structural characterizations of nilpotent hypergroups.

We show that semigroup C*-algebras are groupoid C*-algebras.

We present alternative postulates for Euclidean geometry whose merit is that they lead to a new class of invariants and associated geometries for real finite-dimensional unital associative algebras.

Let $\Gamma$ be a discrete group. To every ideal in $\ell^{\infty}(\G)$ we associate a C$^*$-algebra completion of the group ring that encapsulates the unitary representations with matrix coefficients belonging to the ideal. The general…

This article explains basic constructions and results on group algebras and their cohomology, starting from the point of view of commutative algebra. It provides the background necessary for a novice in this subject to begin reading Dave…

We present groupoid morphisms as an algebraic structure for nonautonomous dynamics, as well as a generalization of group morphisms, which describe classic dynamical systems. We introduce the structure of cotranslations, as a specific kind…

The purpose of this note is twofold. First, we survey results on the construction of large class groups of number fields by specialization of finite covers of curves. Then we give examples of applications of these techniques.