The quantum plane is the non-commutative polynomial algebra in variables x and y with = q . In this paper, we study module variety of n -dimensional modules over plane, provide an explicit description its irreducible components their dimensions. We also describe dimensions GIT quotient respect to conjugation action GL

Theorem. (Auslander-Buchsbaum-Serre, 1956; see [2] and [24].) Let V be an affine algebraic variety over an algebraically closed field with coordinate ring R. Then the global dimension of R is finite if and only if V is smooth. If this is the case, then gl dimR = dimV . (That the global dimension of R is bounded above by n means that n-fold iteration of the process of taking syzygies of R-module...

In this note, we consider the twisted Yangians $\text{Y}(\mathfrak{g}_N)$ associated with orthogonal and symplectic Lie algebras $\mathfrak{g}_N=\mathfrak{o}_N,\mathfrak{sp}_N$. First, introduce a certain subalgebra $\text{A}_c(\mathfrak{g}_N)$ of double Yangian for $\mathfrak{gl}_N$ at level $c\in\mathbb{C}$, which contains centrally extended $c$ as well its vacuum module $\mathcal{M}_c(\mathf...

Background: Gastric lavage (GL) is one of the most commonly used decontamination method for cholinergic insecticide ingestion in developing countries despite lack of supporting evidence. This study was designed to evaluate the outcome of patients with cholinergic insecticide poisoning treated with GL in regards to timing and frequency of the procedure. Methods: In this prospective observational...

We introduce super Yangian double DYh̄[gl(m|n)] and its central extension ̂ DYh̄[gl(m|n)]. We give their defining relations in terms of current generators and obtain Drinfeld comultiplication. Queen Elizabeth II Fellow; Email: [email protected] This paper concerns with Drinfeld current realization [1] of super Yangian double DYh̄[gl(m|n)] and its central extension ̂ DYh̄[gl(m|n)]. The Yangian doubl...

The composition factors of Kac-modules for the general linear Lie superalgebra gl m|n is explicitly determined. In particular, a conjecture of Hughes, King and van der Jeugt in [J. Math. Phys., 41 (2000), 5064-5087] is proved.

The irreducible unitary representations of GL(n, ~) have been classified by D. Vogan in [V2]. In his work, four families of representations play a special role. They are (i) the one dimensional unitary representations and (ii) their complementary series; (iii) Speh's representations and (iv) their complementary series. These representations serve as "building blocks" in the sense that every irr...

The paper is devoted to the study of some important types of minimal artinian linear groups. The authors prove that in such classes of groups as hypercentral groups (so also, nilpotent and abelian groups) and FC-groups, minimal artinian linear groups have precisely the same structure as the corresponding irreducible linear groups. 2000 Mathematics Subject Classification. 20E36, 20F28. Let F be ...

We prove that St(n,A) is a crossed module over GL(n,A) under local stable rank condition on an algebra A commutative ring. Our proof uses only elementary localization techniques in terms of pro-groups and stability results for K1 K2. also similar result the Steinberg group associated with any sufficiently isotropic general linear constructed by quasi-finite algebra.