Related papers: On the categorical behaviour of $V$-groups

A graph $\Gamma$ is called $G$-symmetric if it admits $G$ as a group of automorphisms acting transitively on the set of ordered pairs of adjacent vertices. We give a classification of $G$-symmetric graphs $\Gamma$ with $V(\Gamma)$ admitting…

We study the structure group of a canonical algebraic curvature tensor built from a symmetric bilinear form, and show that in most cases it coincides with the isometry group of the symmetric form from which it is built. Our main result is…

A Chevalley type integral basis for the ortho-symplectic Lie superalgebra is constructed. The simple modules of the ortho-symplectic supergroup over an algebraically closed field of prime characteristic not equal to 2 are classified, where…

In this paper, we describe the Grothendieck groups $K_1(V)$ and $K(V)$ of an absolute matrix order unit space $V$ for unitary and partial unitary elements respectively. For this purpose, we study some basic properties of unitary and partial…

We give a new characterization of partial groups as a subcategory of symmetric (simplicial) sets. This subcategory has an explicit reflection, which permits one to compute colimits in the category of partial groups. We also introduce the…

Let R be a commutative ring with unity, M be an unitary R-module and {\Gamma} be a simple graph. This research article is an interplay of combinatorial and algebraic properties of M . We show a combinatorial object completely determines an…

We prove that the category of quasi-pseudometric modular spaces whose morphisms are the nonexpansive mappings is isomorphic to a quantale enriched category. To achieve this, we construct an appropriate quantale of isotone functions. We also…

Let $\Gamma$ be a hyperbolic group and G be the isometry group of a Gromov-hyperbolic, properand geodesic metric space. We study the action of the outer automorphism group Out($\Gamma$) onthe set X($\Gamma$,G) of conjugacy classes of…

The structure of categorical at zero semigroups is studied from the point of view their likeness to categories.

Let M denote either Euclidean or hyperbolic n-space, and let G be a discrete group of isometries of M, with the property that G respects and acts tile-transitively on a convex-polyhedral tesselation of M. Given an arbitrary base point p in…

Let $\mathbb{H}\trianglelefteq\mathbb{G}$ be a closed normal subgroup of a locally compact quantum group. We introduce a strictly positive group-like element affiliated with $L^{\infty}(\mathbb{G})$ that, roughly, measures the failure of…

We introduce a new cubical model for homotopy types. More precisely, we'll define a category Qs with the following features: Qs is a PROP containing the classical box category as a subcategory, the category Qs-Set of presheaves of sets on…

We give a geometric characterization of finite rational groups. In particular, we prove that a finite group is rational if and only if there exists a finite geometry $\Gamma$ of type $I$ and action of $G$ on $\Gamma$ as a group of…

In this paper, we try to answer the following question: given a modular tensor category $\A$ with an action of a compact group $G$, is it possible to describe in a suitable sense the ``quotient'' category $\A/G$? We give a full answer in…

We first prove that the K-theoretic Hall algebra of a preprojective algebra of affine type is isomorphic to the positive half of a quantum toroidal quantum group. An essential step consists to deform the K-theoretic Hall algebra so that the…

We describe the mathematical properties of pairwise comparisons matrices with coefficients in an arbitrary group. We provide a vocabulary adapted for the description of main algebraic properties of inconsistency maps, describe an example…

For the algebra $A$ in the title, its prime, primitive and maximal spectra are classified. The group of automorphisms of $A$ is determined. The simple unfaithful $A$-modules and the simple weight $A$-modules are classified.

Complete MV-algebras are naturally equipped with frame structures. We call them MV-frames and investigate some of their main the properties as frames. We completely characterized algebraic MV-frames as well as regular MV-frames. In…

This is an expository book on unitary representations of topological groups, and of several dual spaces, which are spaces of such representations up to some equivalence. The most important notions are defined for topological groups, but a…

Let p be a prime, G a locally finite p-group, K a commutative ring of characteristic p. The anti-automorphism g\mapsto g\m1 of G extends linearly to an anti-automorphism a\mapsto a^* of KG. An element a of KG is called symmetric if a^*=a.…