Related papers: Split extensions and semidirect products of unitar…

We introduce a novel concept of action for unitary magmas, facilitating the classification of various split extensions within this algebraic structure. Our method expands upon the recent study of split extensions and semidirect products of…

A generalization to the categorical notion of biproduct, called semibiproduct, which in the case of groups covers classical semidirect products, has recently been analysed in the category of monoids with surprising results in the…

We investigate the behaviour of split extensions in the category OrdGrp of (pre)\-ordered groups. Namely we show that the lexicographic order plays a key role on the existence of compatible orders for semidirect products, establishing…

Semibiproducts of monoids are introduced here as a common generalization to biproducts (of abelian groups) and to semidirect products (of groups) for exploring a wide class of monoid extensions. More generally, abstract semibiproducts exist…

We investigate the homological behaviour of compactly generated triangulated categories under separable extensions. We show that homological invariants (finiteness of global dimension, gorensteinness and regularity) are preserved under such…

We consider monoids equipped with a compatible quantale valued relation, to which we call quantale enriched monoids, and study semidirect products of such structures. It is well-known that semidirect products of monoids are closely related…

We develop a theory of separable ring extensions and separable functors for nonunital rings in the setting of firm modules. We prove nonunital analogues of classical results on functorial separability and semisimplicity, and apply these…

We introduce the concept of an extension of a semilattice of groups $A$ by a group $G$ and describe all the extensions of this type which are equivalent to the crossed products $A*_\Theta G$ by twisted partial actions $\Theta$ of $G$ on…

A permutation class is splittable if it is contained in the merge of two of its proper subclasses. We characterise the unsplittable subclasses of the class of separable permutations both structurally and in terms of their bases.

We extend the classical construction by Noether of crossed product algebras, defined by finite Galois field extensions, to cover the case of separable (but not necessarily finite or normal) field extensions. This leads us naturally to…

The semigroups of unital extensions of separable $C^\ast$-algebras come in two flavours: a strong and a weak version. By the unital $\mathrm{Ext}$-groups, we mean the groups of invertible elements in these semigroups. We use the unital…

We prove a structure result on proper extensions of two-sided restriction semigroups in terms of partial actions, generalizing respective results for monoids and for inverse semigroups and upgrading the latter. We introduce and study…

Let S be a site. We introduce the notion of extensions of strictly commutative Picard S-stacks. We define the pull-back, the push-down, and the sum of such extensions and we compute their homological interpretation: if P and Q are two…

Semigroup actions and their invertible extensions are discussed. First, we develop a theory of natural extensions for continuous actions of countable, embeddable semigroups. Second, we demonstrate that not every surjective such action of a…

We characterize the group property of being with infinite conjugacy classes (or icc, i.e. in which all conjugacy classes beside 1 are infinite) for split extensions of groups.

Let $B$ be the one-point extension algebra of $A$ by an $A$-module $M$. We proved that every ICE-closed subcategory in$\mod A$ can be extended to be some ICE-closed subcategories in$\mod B$.In the same way, every epibrick in $\mod A$ can be…

In this paper, nil extensions of some special type of ordered semigroups, such as, simple regular ordered semigroups, left simple and right regular ordered semigroup. Moreover, we have characterized complete semilattice decomposition of all…

We study unitary representations of semidirect products of a compact quantum group with a finite group. We give a classification of all irreducible unitary representations, a description of the conjugate representation of irreducible…

We show a stability-type theorem for foliations on projective spaces which arise as pullbacks of foliations with a split tangent sheaf on weighted projective spaces. As a consequence, we will be able to construct many irreducible components…

This article is devoted to the investigation of semidirect products of groups of loops and groups of diffeomorphisms of finite and infinte dimensional real, complex and quaternion manifolds. Necessary statements about quaternion manifolds…