Related papers: Left equalizer simple semigroups

We begin a systematic study of finite semigroups that generate join irreducible members of the lattice of pseudovarieties of finite semigroups, which are important for the spectral theory of this lattice. Finite semigroups $S$ that generate…

Let $D$ be division algebra over its center $C$, let $\sigma$ be an endormorphism of $D$, let $\delta$ be a left $\sigma$-derivation of $D$, and let $R=D[t;\sigma,\delta]$ be a skew polynomial ring. We study the structure of a class of…

Semifields are semirings in which every nonzero element has a multiplicative inverse. A rough classification uses the characteristic of the semifield, that is the isomorphism type of the semifield generated by the two neutral elements. For…

Let $G$ be a finite group. There is a standard theorem on the classification of $G$-equivariant finite dimensional simple commutative, associative, and Lie algebras (i.e., simple algebras of these types in the category of representations of…

We classify semisimple left module categories over the representation category of a type A quantum group whose fusion rules arise from the maximal torus. The classification is connected to equivariant Poisson structures on compact full flag…

Let $F \ast G$ be a free product of a free group $F$ and a LERF group $G$. In this note, we provide sufficient conditions for a subgroup $H$ of $F \ast G$ to be $\mathcal{A} \cup \mathcal{S}$-separable, that is, for any finite set…

For a left coherent ring A with every left ideal having a countable set of generators, we show that the coderived category of left A-modules is compactly generated by the bounded derived category of finitely presented left A-modules…

Consider the Iwasawa decomposition of the real semisimple Lie group. The purpose of this paper is to define the Fourier transform in order to obtain the Plancherel theorem on its maxima solvable Lie group. Besides, we prove the existence…

For G a group and g in G, we define mappings pg(G) and lg(G) from G into G by pg(x)=[x,g] and lg(x)=[g,x]. We let P(G) and L(G) denote the subsemigroups of the set of all mappings from G to G generated by {pg: g in G} and {lg: g in G},…

In this article, we study the elements with disconnected centralizer in the Brauer complex associated to a simple algebraic group G defined over a finite field with corresponding Frobenius map F and derive the number of F-stable semisimple…

Let $R$ be a ring, $\CC_R$ and $\pCCR$ be the set of regular and left regular elements of $R$ ($\CC_R\subseteq \pCCR$). Goldie's Theorem is a semisimplicity criterion for the classical left quotient ring $Q_{l,cl}(R):=\CC_R^{-1}R$.…

It is proved that, given a (von Neumann) regular semigroup with finitely many left and right ideals, if every maximal subgroup is presentable by a finite complete rewriting system, then so is the semigroup. To achieve this, the following…

A DR-semigroup $S$ (also known as a reduced E-semiabundant or reduced E-Fountain semigroup) is here viewed as a semigroup equipped with two unary operations $D,R$ satisfying finitely many equational laws. Examples include DRC-semigroups…

We introduce a class of left ideals (and subalgebras) of nest algebras determined by totally ordered families of partial isometries on a complex Hilbert space $H$. Let $\mathcal{E}$ be a family of partial isometries that is totally ordered…

Let $G$ be a group and let $\rho\colon G\to\operatorname{Sym}(V)$ be a permutation representation of $G$ on a set $V$. We prove that there is a faithful $G$-coalgebra $C$ such that $G$ arises as the image of the restriction of…

We classify skew braces that are the semidirect product of an ideal and a left ideal. As a consequence, given a Galois extension of fields $ L/K $ whose Galois group is the semidirect product of a normal subgroup $ A $ and a subgroup $ B $,…

Let $[n]=\{1,2,\ldots,n\}$ be a finite chain and let $\mathcal{T}_{n}$ be the semigroup of full transformations on $[n]$. Let $\mathcal{CT}_{n}=\{\alpha\in \mathcal{T}_{n}: (for ~all~x,y\in…

We study left-invariant foliations ${\mathcal F}$ on semi-Riemannian Lie groups $G$ generated by a subgroup $K$. We are interested in such foliations which are conformal and with minimal leaves of codimension two. We classify such…

This paper contains several results about the structure of the congruence kernel C^(S)(G) of an absolutely almost simple simply connected algebraic group G over a global field K with respect to a set of places S of K. In particular, we show…

Let $G$ be the universal Chevalley-Demazure group scheme corresponding to a reduced irreducible root system of rank $\geq 2$, and let $R$ be a commutative ring. We analyze the linear representations $\rho \colon G(R)^+ \to GL_n (K)$ over an…