Related papers: Polyadic analogs of direct product
A \emph{loop} $(B,\cdot)$ is a set $B$ together with a binary operation $\cdot$ such that (i) for each $a\in B$, the left and right translation mappings $L_{a}:B\to B: x \mapsto a\cdot x$ and $R_{a}:B\to B: x \mapsto x\cdot a$ are…
Nonuniqueness of semidirect decompositions of groups is an insufficiently studied question in contrast to direct decompositions. We obtain some results about semidirect decompositions for semidirect products with factors which are…
A product of cochains in a polyhedral complex is constructed. The multiplication algorithm depends on the choice of a parameter. The parameter is a linear functional on the ambient space. Cocycles form a subring of the ring of cochains,…
Let L be the generalized mixed product ideal induced by a monomial ideal I. In this paper, we study the polymatroidal property of generalized mixed product ideals. Furthermore, some algebraic invariants of L are computed.
The notion of a generalized product, refining that of a (symmetric and smooth) simplicial space is introduced and shown to imply the existence of an algebra of pseudodifferential operators. This encompasses many constructions of such…
It is shown that the category of \emph{semi-biproducts} of monoids is equivalent to the category of \emph{pseudo-actions}. A semi-biproduct of monoids is a new notion, obtained through generalizing a biproduct of commutative monoids. By…
In this article we put a very elaborate PSH-like structure on the $R_{+}(-)$ groups of products of finite general linear groups. This is not the case we want. Firstly one would really want the actual big PSH algebra of products of general…
In this book i treat linear algebra over division ring. A system of linear equations over a division ring has properties similar to properties of a system of linear equations over a field. However, noncommutativity of a product creates a…
The study of images of noncommutative polynomials on algebras has attracted considerable attention. We investigate polynomial images and the additive structures they generate in associative algebras, focusing on sums and products of values.…
We introduce G{\aa}rding polynomials, a class of real multivariate polynomials characterized by positivity regions that are invariant under translation by positive vectors and closed under strictly positive affine transformations. We prove…
We apply the free product construction to various local algebras in algebraic quantum field theory. If we take the free product of infinitely many identical half-sided modular inclusions with ergodic canonical endomorphism, we obtain a…
Generalizing a theorem of Macdonald, we show a formula for the mixed Hodge structure on the cohomology of the symmetric products of bounded complexes of mixed Hodge modules by showing the existence of the canonical action of the symmetric…
One of pressing problems in mathematical physics is to find a generalized Poincar\'e symmetry that could be applied to nonflat space-times. As a step in this direction we define the semidirect product of groupoids $\Gamma_0 \rtimes…
The main aim of this paper is to determine the multiplicative lie algebra structures on the semi-direct product of an abelian group with a group under certain conditions.
We introduce a new class of groups called wreath-like products. These groups are close relatives of the classical wreath products and arise naturally in the context of group theoretic Dehn filling. Unlike ordinary wreath products, many…
Coset geometries are incidence geometries constructed from a group $G$ and a system of subgroups $(G_i)_{i \in I}$ of subgroups of $G$. For any algebraic group operation, it is then natural to wonder whether it can be extended to the…
Products and coproducts may be recognized as morphisms in a monoidal tensor category of vector spaces. To gain invariant data of these morphisms, we can use singular value decomposition which attaches singular values, ie generalized…
The Hadamard quasigroup product has recently been introduced as a natural generalization of the classical Hadamard product of matrices. It is defined as the superposition operator of three binary operations, one of them being a quasigroup…
We introduce semidirect products of skew monoidal categories as a categorification of semidirect products of monoids (or, perhaps more familiarly, of groups). We also discuss how this construction interacts with monoidal, autonomous and…
Semi-direct products of finite groups have permutation representations that are constructed from the permutation representations of their constituents. One can envision these in a metaphoric sense in which a rope is made from a bundle of…