One problematic feature of Hall algebras is the fact that the standard multiplication and comultiplication maps do not satisfy the bialgebra compatibility condition in the underlying symmetric monoidal category Vect. In the past this problem has been resolved by working with a weaker structure called a ‘twisted’ bialgebra. In this paper we solve the problem differently by first switching to a d...

This work was started as an attempt to apply theory from noncommutative graded algebra to questions about the holonomy algebra of a hyperplane arrangement. We soon realized that these algebras and their deformations, which form a class of quadratic graded algebras, have not been studied much and yet are interesting to algebra, arrangement theory and combinatorics. Let X be a topological space h...

In 2021, Dzhunusov and Zaitseva classified two-dimensional normal affine commutative algebraic monoids. this work, we extend classification to noncommutative monoid structures on surfaces. We prove that monoids are toric. also show how find all a toric surface. Every such structure is induced by comultiplication formula involving Demazure roots. give descriptions of opposite monoids, quotient b...

Abstract. Let (R,P) be a Noetherian unique factorization do-main (UFD) and M be a finitely generated R-module. Let I(M)be the first nonzero Fitting ideal of M and the order of M, denotedord_R(M), be the largest integer n such that I(M) ⊆ P^n. In thispaper, we show that if M is a module of order one, then either Mis isomorphic with direct sum of a free module and a cyclic moduleor M is isomorphi...

let $r$ be a right artinian ring or a perfect commutative‎‎ring‎. ‎let $m$ be a noncosingular self-generator $sum$-lifting‎‎module‎. ‎then $m$ has a direct decomposition $m=oplus_{iin i} m_i$‎,‎where each $m_i$ is noetherian quasi-projective and each‎‎endomorphism ring $end(m_i)$ is local‎.

We discuss an example of a triangulated Hopf category related to SL(2). It is an equivariant derived category equipped with multiplication and comultiplication functors and structure isomorphisms. We prove some coherence equations for structure isomorphisms. In particular, the Hopf category is monoidal.

We give an explicit criterion for the irreducibility of some induction products of evaluation modules of affine Hecke algebras of type A. This allows to describe the form of the zeros and poles of the trigonometric R-matrix associated to any evaluation module of Uv(ŝlN ). Abridged english version — Let Ĥn(u) be the affine Hecke algebra associated to GL(n) and Hn(u) its finite-dimensional subalg...

Abstract:  Introduction: The current study as a part of our investigation on improving emotional and behavioural health in Malaysian orphanages was aimed to establish Content Validity Index (CVI) as well as Face Validity of a new life skill-based module for improving emotional health and coping mechanisms in Malaysian Institutionalised Adolescents including 2 different parts. Methods: In...