Related papers: An explicit construction of simple-minded systems …

Let $A$ be a representation-finite self-injective algebra over an algebraically closed field $k$. We give a new characterization for an orthogonal system in the stable module category $A$-$\stmod$ to be a simple-minded system. As a…

Simple-minded systems of objects in a stable module category are defined by common properties with the set of simple modules, whose images under stable equivalences do form simple-minded systems. Over a representation-finite self-injective…

We study the relation between simple-minded systems and two-term tilting complexes for self-injective Nakayama algebras. More precisely, we show that any simple-minded system of a self-injective Nakayama algebra is the image of the set of…

Simple-minded systems in stable module categories are defined by orthogonality and generating properties so that the images of the simple modules under a stable equivalence form such a system. Simple-minded systems are shown to be invariant…

Tachikawa's second conjecture predicts that a finitely generated, orthogonal module over a finite-dimensional self-injective algebra is projective. This conjecture is an important part of the Nakayama conjecture. Our principal motivation of…

Let $A$ be a 2-domestic Brauer graph algebra. We present a construction for a family of objects on $A$-$\stmod$ to be a simple-minded system and our construction provides all simple-minded systems on $A$-$\stmod$. As a byproduct, we provide…

Let A be a selfinjective algebra. We show that, for any n, maximal n-orthogonal A-modules (in the sense of Iyama), rarely exist. More precisely, we prove that if A admits a maximal n-orthogonal module, then all A-modules are of complexity…

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 $\mathcal{S}$…

Let $A$ be a finite dimensional algebra over an algebraically closed field. We present a relationship between simple-minded systems and coherent rings.

Enomoto showed for finite dimensional algebras that the classification of exact structures on the category of finitely generated projective modules can be reduced to the classification of 2-regular simple modules. In this article, we give a…

The stable module category has been realized as a subcategory of the unbounded homotopy category of projective modules by Kato. We construct the triangulated hull of this subcategory inside the homotopy category. This can also be used to…

We describe the structure of finite dimensional selfinjective algebras over an arbitrary field without short cycles of indecomposable modules.

Let $\Lambda$ be a radical square zero Nakayama algebra with $n$ simple modules and let $\Gamma$ be the Auslander algebra of $\Lambda$. Then every indecomposable direct summand of a tilting $\Gamma$-module is either simple or projective.…

Let A be a finite-dimensional algebra. If A is self-injective, then all modules are reflexive. Marczinzik recently has asked whether A has to be self-injective in case all the simple modules are reflexive. Here, we exhibit an 8-dimensional…

The paper describes the algebraic structure of the graded algebra of differentially homogeneous polynomials of fixed finite order. We show that it is a finitely generated algebra, and we exhibit a minimal set of generators. Along the way,…

Motivated by understanding the Nakayama conjecture which states that algebras of infinite dominant dimension should be self-injective, we study self-orthogonal modules with virtually Gorenstein endomorphism algebras and prove the following…

This work is an attempt towards a Morita theory for stable equivalences between self-injective algebras. More precisely, given two self-injective algebras A and B and an equivalence between their stable categories, consider the set S of…

The stable module category of a selfinjective algebra is triangulated, but need not have any nontrivial $t$-structures, and in particular, full abelian subcategories need not arise as hearts of a $t$-structure. The purpose of this paper is…

We show that the Calabi-Yau dimension of the stable module category of a selfinjective algebra of finite representation type is determined by the action of the Nakayama and suspension functors on objects. Our arguments are based on recent…

We determine the derived representation type of Nakayama algebras and prove that a derived tame Nakayama algebra without simple projective module is gentle or derived equivalent to some skewed-gentle algebra, and as a consequence, we…