Related papers: A Note on Semigroup Algebras of Permutable Semigro…

We study the spectra of non-regular semisimple elements in irreducible representations of simple algebraic groups. More precisely, we prove that if G is a simply connected simple linear algebraic group and f is a non-trivial irreducible…

A closed subgroup of a semisimple algebraic group is called irreducible if it lies in no proper parabolic subgroup. In this paper we classify all irreducible $A_1$ subgroups of exceptional algebraic groups $G$. Consequences are given…

It is an open question whether the smash product of a semisimple Hopf algebra and a semiprime module algebra is semiprime. In this paper we show that the smash product of a commutative semiprime module algebra over a semisimple cosemisimple…

Let $G$ be a linear algebraic group over an algebraically closed field of characteristic $p\geq 0$. We show that if $H_1$ and $H_2$ are connected subgroups of $G$ such that $H_1$ and $H_2$ have a common maximal unipotent subgroup and…

We analyze the dichotomy amenable/paradoxical in the context of (discrete, countable, unital) semigroups and corresponding semigroup rings. We consider also F{\o}lner's type characterizations of amenability and give an example of a…

The endomorphism algebras of the permutation modules for transitive permutation groups, known as Hecke algebras, are fundamental objects in representation theory. While group algebras are known to be symmetric over any field, it is natural…

We describe $\sigma$-matching, interchangeable and, as a consequence, totally compatible products on some classes of associative algebras, including unital algebras, the semigroup algebras of rectangular bands, algebras with enough…

A regular ordered semigroup $S$ is called right inverse if every principal left ideal of $S$ is generated by an $\mathcal{R}$-unique ordered idempotent. Here we explore the theory of right inverse ordered semigroups. We show that a regular…

Suppose $G$ is a finitely presented group that is hyperbolic relative to ${\bf P}$ a finite collection of 1-ended finitely generated proper subgroups of $G$. If $G$ and the ${\bf P}$ are 1-ended and the boundary $\partial (G,{\bf P})$ has…

Let G be a finite group and {\sigma} = {{\sigma}_i, i \in I} be a partition of the set of all primes \mathbb{P}. A set \mathcal{H} of subgroups of G with 1 \in \mathcal{H} is said to be a complete Hall {\sigma}-set of G if every…

This paper is a contribution to the theory of finite semigroups and their classification in pseudovarieties, which is motivated by its connections with computer science. The question addressed is what role can play the consideration of an…

A free semigroup algebra S is the weak-operator-closed (non-self-adjoint) operator algebra generated by n isometries with pairwise orthogonal ranges. A unit vector x is said to be wandering for S if the set of images of x under…

Assume $G$ is a definable group in a stable structure $M$. Newelski showed that the semigroup $S_G(M)$ of complete types concentrated on $G$ is an inverse limit of the $\infty$-definable (in $M^{eq}$) semigroups $S_{G,\Delta}(M)$. He also…

A semigroup $S$ is called a weakly exponential semigroup if, for every couple $(a,b)\in S\times S$ and every positive integer $n$, there is a non-negative integer $m$ such that $(ab)^{n+m}=a^nb^n(ab)^m=(ab)^ma^nb^n$. A semigroup $S$ is…

In this paper we seek to determine the Jacobson radical of certain algebras based on semigroups, and in particular on the semigroups $(\beta S, \Box)$, where $S$ is a cancellative, countable, abelian semigroup and $\beta S$ is its…

Let $\sigma =\{\sigma_{i} | i\in I\}$ be a partition of the set of all primes $\Bbb{P}$ and $G$ a finite group. A set ${\cal H}$ of subgroups of $G$ is said to be a \emph{complete Hall $\sigma $-set} of $G$ if every member $\ne 1$ of ${\cal…

We introduce locally involutive semigroups and embed them into the category of ordered groupoids. This embedding restricts to a correspondence between quasi-involutive semigroups and ordered groupoids with mediator, extending the classical…

'A semigroup is completely regular if and only if it is a union of groups'- an analogue of this structure theorem of completely regular semigroup has been obtained in the setting of seminearrings in [[16], Mukherjee (Pal) et al., Semigroup…

Here we characterize regular and completely regular ordered semigroups by their minimal bi-ideals. A minimal bi-ideal is expressed as a product of a minimal right ideal and a minimal left ideal. Furthermore, we show that every bi-ideal in a…

Let $S$ be a semitopological semigroup and $\mathcal{CB}(S)$ denotes the $C^*$-algebra of all bounded complex valued continuous functions on $S$ with uniform norm. A function $f\in \mathcal{CB}(S)$ is left multiplicative \linebreak…