相关论文: Groups up to congruence relation and from categori…

We present some constructions of groupoids as: direct product, semidirect product, and we give necessary and sufficient conditions for a groupoid to be embedded into a direct product of groupoids. Also, we establish necessary and sufficient…

We survey the extensions of a group by a group using crossed products instead of exact sequences of groups. The approach has various advantages, one of them being that the crossed product is an universal object. Several new applications are…

In this article, we introduce the concepts of graded $s$-prime submodules which is a generalization of graded prime submodules. We study the behavior of this notion with respect to graded homomorphisms, localization of graded modules,…

The purpose of this note is to observe that a homomorphism of discrete groups $f:\Gamma\to G$ arises as the induced map $\pi_0(\mathfrak{M})\to \pi_0(\mathfrak{X})$ on path components of some closed normal inclusion of topological groups…

We introduce the notion of 3-crossed module, which extends the notions of 1-crossed module (Whitehead) and 2-crossed module (Conduch\'e). We show that the category of 3-crossed modules is equivalent to the category of simplicial groups…

This is the second part of the paper. Results of the first part about crossed modules are applied here to study of quantum groups in braided categories. Correct cross product in the class of quantum braided groups is built. Criterion when…

A crossed module is (A,H,d,\la) where d:A\to H is a homomorphism of groups and H acts on A, with conditions leading to a groupoid A\lcross H{\to\atop \to}H as an example of a strict 2-group. We give the corresponding notion of a quantum…

For a free partial action of a group in a set we realize the associated partial skew group ring as an algebra of functions with finite support over an equivalence relation and we use this result to characterize the ideals in the partial…

We study actions of discrete groups on 2-categories. The motivating examples are actions on the 2-category of representations of finite tensor categories and their relation with the extension theory of tensor categories by groups.…

In this paper we explore the structure and properties of C-groups. We define a C-group as a group $G$ with $rk(G) < rk(Z(G))$ (where $rk(G)$ is the minimal cardinal of a generating set for a group $G$). Using GAP (a group theory program)…

Let $H$ be a Hopf algebra in braided category $\cal C$. Crossed modules over $H$ are objects with both module and comodule structures satisfying some comatibility condition. Category ${\cal C}^H_H$ of crossed modules is braided and is…

The semidirect product of a finitely generated group dual with the symmetric group can be described through so-called group-theoretical categories of partitions (covers only a special case; due to Raum--Weber, 2015) and skew categories of…

We use quasi-orders to describe the structure of C-groups. We do this by associating a quasi-order to each compatible C-relation of a group, and then give the structure of such quasi-ordered groups. We also reformulate in terms of…

In this paper we define the notions of normal subcrossed module and quotient crossed module within groups with operations; and using the equivalence of crossed modules over groups with operations and internal groupoids we prove how…

We review the notions of a multiplier category and the $W^{*}$-envelope of a $C^{*}$-category. We then consider the notion of an orthogonal sum of a (possibly infinite) family of objects in a $C^{*}$-category. Furthermore, we construct…

We introduce the notion of a ``sofic $\mathcal{C}$-action'' of one group on another by automorphisms, for $\mathcal{C}$ a class of groups. We show that if $\mathcal{C}$ is the class of (i) sofic, (ii) hyperlinear, (iii) linear sofic or (iv)…

Several authors have introduced various type of coherent-like rings and proved analogous results on these rings. It appears that all these relative coherent rings and all the used techniques can be unified. In [2], several coherent-like…

We introduce the notion of a crossed product of an algebra by a coalgebra $C$, which generalises the notion of a crossed product by a bialgebra well-studied in the theory of Hopf algebras. The result of such a crossed product is an algebra…

We develop a unified framework based on topological crossed modules for various lifting obstructions for $\Gamma$-kernels. It allows us to identify actions, cocycle actions and $\Gamma$-kernels up to their natural equivalence relations with…

In this paper we present the construction of explicit quasi-isomorphisms that compute the cyclic homology and periodic cyclic homology of crossed-product algebras associated with (discrete) group actions. In the first part we deal with…