Related papers: Nil extensions of Clifford ordered semigroup

Let $[n]=\{1,2,\ldots,n\}$ be a finite chain and let $\mathcal{P}_{n}$ be the semigroup of partial transformations on $[n]$. Let $\mathcal{CP}_{n}=\{\alpha\in \mathcal{P}_{n}: (for ~all~x,y\in Dom~\alpha)~|x\alpha-y\alpha|\leq|x-y|\}$ be…

Real Clifford algebras for arbitrary number of space and time dimensions as well as their representations in terms of spinors are reviewed and discussed. The Clifford algebras are classified in terms of isomorphic matrix algebras of real,…

We investigate the maximum length of a chain of subsemigroups in various classes of semigroups, such as the full transformation semigroups, the general linear semigroups, and the semigroups of order-preserving transformations of finite…

We give some examples of, and raise some questions on, extensions of semisimple Hopf algebras.

This paper is a continuation of the paper [arXiv:0911.4725], investigating a natural radial deformation of the Fourier transform in the setting of Clifford analysis. At the same time, it gives extensions of many results obtained in…

We introduce the notion of an oriented Steiner quasigroup and develop elements of a relevant algebraic apparatus. The approach is based upon (modified) Schreier-type $f$-extensions for quasigroups (cf. earlier works \cite{S, NSt, NSt2})…

In this paper we classify extensions between irreducible finite conformal modules over the Virasoro algebra, over the current algebras and over their semidirect sums.

In this paper we further develop the method of quaternion typification of Clifford algebra elements suggested by the author in the previous paper. On the basis of new classification of Clifford algebra elements it is possible to reveal and…

It is known that the behavior of the Mitchell order substantially changes at the level of rank-to-rank extenders, as it ceases to be well-founded. While the possible partial order structure of the Mitchell order below rank-to-rank extenders…

Clifford theory establishes a relation between the representation theory of a finite group and its normal subgroups. In this paper, we establish the Clifford theory for the modular representations of finite groups. The proofs are based on…

Let $Q$ be an inverse semigroup. A subsemigroup $S$ of $Q$ is a left I-order in $Q$ and $Q$ is a semigroup of left I-quotients of $S$ if every element in $Q$ can be written as $a^{-1}b$, where $a, b \in S$ and $a^{-1}$ is the inverse of $a$…

Although Clifford analysis is like complex analysis in many ways, there are obvious differences related to noncommutativity, and a few aspects of this are considered here.

Groups, in which every subgroup containing some fixed primary cyclic subgroup has a complement, are investigated.

We present a new classification of Clifford algebra elements. Our classification is based on the notion of quaternion type. Using this classification we develop a method for analyzing of commutators and anticommutators of Clifford algebra…

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…

All isolated, completely isolated, and nilpotent subsemigroups in the semigroup $\IS$ of all injective partial transformations of an $n$-element set, considered as a semigroup with a sandwich multiplication are described.

In this paper we present an approach to quadratic structures in derived algebraic geometry. We define derived n-shifted quadratic complexes, over derived affine stacks and over general derived stacks, and give several examples of those. We…

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…

The present article is a part of the study of solvable Leibniz algebras with a given nilradical. In this paper solvable Leibniz algebras, whose nilradicals is naturally graded quasi-filiform algebra and the complemented space to the…

Let $\mathcal{CP}_n$ be the semigroup of partial contraction mappings on $[n]=\{1,2,\ldots,n\}$ and let $\mathcal{OCP}_n$ and $\mathcal{ORCP}_n$ be its subsemigroups consisting of all order-preserving and of all order-preserving or…