Related papers: Endomorphism rings of permutation modules over max…

Denote by PSelf(X) (resp., Self(X)) the partial (resp., full) transformation monoid over a set X, and by Sub(V) (resp., End(V)) the collection of all subspaces (resp., endomorphisms) of a vector space V. We prove various results that imply…

The aim of this article is to investigate central-valued identities involving pairs of endomorphisms on prime rings equipped with an involution of the second kind. Extending the recent contributions of Mir et al. (2020) and Boua et al.…

Inspired by the work [PA], we establish an explicit algebra isomorphism between the degenerate cyclotomic Yokonuma-Hecke algebra $Y_{r,n}^{d}(q)$ and a direct sum of matrix algebras over tensor products of degenerate cyclotomic Hecke…

We give a presentation of the endomorphism algebra $\End_{\cU_q(\fsl_2)}(V^{\otimes r})$, where $V$ is the 3-dimensional irreducible module for quantum $\fsl_2$ over the function field $\C(q^{{1/2}})$. This will be as a quotient of the…

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…

Motivated by the relation between Schur algebra and the group algebra of a symmetric group, along with other similar examples in algebraic Lie theory, Min Fang and Steffen Koenig addressed some behaviour of the endomorphism algebra of a…

The category of all $k$-algebras with a bilinear form, whose objects are all pairs $(R,b)$ where $R$ is a $k$-algebra and $b\colon R\times R\to k$ is a bilinear mapping, is equivalent to the category of unital $k$-algebras $A$ for which the…

Let $R_n$ denote the KLR algebra of type $A^{(1)}_{e-1}$. Using the presentation of Specht modules given by Kleschev-Mathas-Ram, Loubert completely determined $\hom_{R_n}(S^\mu,S^\lambda)$ where $\mu$ is an arbitrary partition, $\lambda$ is…

Given a transitive permutation group, a fundamental object for studying its higher transitivity properties is the permutation action of its isotropy subgroup. We reverse this relationship and introduce a universal construction of infinite…

A metacyclic group $H$ can be presented as $\langle \alpha,\beta\mid \alpha^{n}=1, \ \beta^{m}=\alpha^{t}, \ \beta\alpha\beta^{-1}=\alpha^{r}\rangle$ for some $n,m,t,r$. Each endomorphism $\sigma$ of $H$ is determined by…

We show that the signed $p$-Kostka numbers depend just on $p$-Kostka numbers and the multiplicities of projective indecomposable modules in certain signed Young permutation modules. We then examine the signed $p$-Kostka number…

There are well-known constructions relating ring epimorphisms and tilting modules. The new notion of silting module provides a wider framework for studying this interplay. To every partial silting module we associate a ring epimorphism…

Over fields of characteristic $2$, Specht modules may decompose and there is no upper bound for the dimension of their endomorphism algebra. A classification of the (in)decomposable Specht modules and a closed formula for the dimension of…

Let $Q$ be a finite quiver of Dynkin type and $\Lambda=\Lambda_Q$ be the preprojective algebra of $Q$ over an algebraically closed field $k$. Let $\mathcal {T}_\Lambda$ be the mutation graph of maximal rigid $\Lambda$ modules. Geiss,…

We establish an algebra-isomorphism between the complexified Grothendieck ring F of certain bimodule categories over a modular tensor category and the endomorphism algebra of appropriate morphism spaces of those bimodule categories. This…

In this paper, we provide several new characterizations of the maximal right ring of quotients of a ring by using the relatively dense property. As a ring is embedded in its maximal right ring of quotients, we show that the endomorphism…

Let $\mathbb{F}$ be a field and let $E$ be the natural representation of $\mathrm{SL}_2(\mathbb{F})$. Given a vector space $V$, let $\Delta^{(2,1^{N-1})}V$ be the kernel of the multiplication map $\bigwedge^N V \otimes V \rightarrow…

For $ k \in \mathbb{N}$ we introduce an idempotent subalgebra, the spherical partition algebra ${\mathcal{SP} }_{k}$, of the partition algebra ${\mathcal{P} }_{k}$, that we define using an embedding associated with the trivial…

In the paper, we consider the class of so-called endo-commutative algebras. From the identity imposed to specify this class, one can easily see that the product in this class preserves the square of elements. We give a complete…

We investigate in detail a homomorphism which we call the 2-Selmer signature map from the $2$-Selmer group of a number field $K$ to a nondegenerate symmetric space, in particular proving the image is a maximal totally isotropic subspace.…