Related papers: Simple reflexive modules over finite-dimensional a…
In this paper, we introduce the concept of JReject of a class of modules as a generalization of the notion of reject of a class of modules. We also introduce the notion of J-torsionless modules and give a characterization of regularity on…
Generalized Heisenberg algebras $\H(f)$ for any polynomial $f(h)\in\C[h]$ have been used to explain various physical systems and many physical phenomena for the last 20 years. In this paper, we first obtain the center of $\H(f)$, and the…
Reflexive functors of modules naturally appear in Algebraic Geometry, mainly in the theory of linear representations of group schemes, and in "duality theories". In this paper we study and determine reflexive functors and we give many…
Let $A$ be a finite-dimensional self-injective algebra over an algebraically closed field, $\mathcal{C}$ a stably quasi-serial component (i.e. its stable part is a tube) of rank $n$ of the Auslander-Reiten quiver of $A$, and $\mathcal{S}$…
The simplicity of the induced modules for reductive Lie algebras over an algebraically closed field of positive characteristic is studied, and a necessary and sufficient condition for the simplicity is given.
In this paper, we first show that for an acyclic gentle algebra A, the irreducible components of any moduli space of A-modules are products of projective spaces. Next, we show that the nice geometry of the moduli spaces of modules of an…
Let $A$ be a tubular algebra and let $r$ be a positive irrational. Let ${\mathcal D}_r$ be the definable subcategory of $A$-modules of slope $r$. Then the width of the lattice of pp formulas for ${\mathcal D}_r$ is $\infty$. It follows that…
We study some aspects of reflexive modules. For example, we search conditions for which reflexive modules are free or being very close to free modules.
Let A be a connected hereditary artin algebra. We show that the set of functorially finite torsion classes of A-modules is a lattice if and only if A is either representation-finite (thus a Dynkin algebra) or A has only two simple modules.…
In this paper we explore the possibility of endowing simple infinite-dimensional ${\mathfrak{sl}_2(\mathbb{C})}$-modules by the structure of the graded module. The gradings on finite-dimensional simple module over simple Lie algebras has…
We survey noetherian rings $A$ over which the injective hull of every simple module is locally artinian. Then we give a general construction for algebras $A$ that do not have this property. In characteristic 0, we also complete the…
In this note, it is proved that over a commutative noetherian henselian non-Gorenstein local ring there are infinitely many isomorphism classes of indecomposable totally reflexive modules, if there is a nonfree cyclic totally reflexive…
We prove a tight connection between reflexive modules over a one-dimensional ring $R$ and its birational extensions that are self-dual as $R$-modules. Consequently, we show that a complete local reduced Arf ring has finitely many…
We construct affine algebras with an arbitrary amount of simple modules of each dimension.
An important problem in the representation theory of affine and toroidal Lie algebras is to classify all possible irreducible integrable modules with finite dimensional weight spaces. Recently the irreducible integrable modules having…
We show that the common theory of all modules over a tubular algebra (over a recursive algebraically closed field) is decidable. This result supports a long standing conjecture of Mike Prest which says that a finite-dimensional algebra…
Recent works of the authors have demonstrated the usefulness of considering moduli spaces of Artinian reductions of a given ring when studying standard graded rings and their Lefschetz properties. This paper illuminates a key aspect of…
A subalgebra $\mathcal{A}$ of a $C^*$-algebra $\mathcal{M}$ is logmodular (resp. has factorization) if the set $\{a^*a; a\text{ is invertible with }a,a^{-1}\in\mathcal{A}\}$ is dense in (resp. equal to) the set of all positive and…
We say that an algebra A is periodic if it has a periodic projective resolution as an (A,A)-bimodule. We show that any self-injective algebra of finite representation type is periodic. To prove this, we first apply the theory of smash…
We denote by $\mathcal{W}$ the class of all pure projective modules. Present article we investigate $\mathcal{W}$-injective modules and these modules are defined via the vanishing of cohomology of pure projective modules. First we prove…