Related papers: Extending ($\tau$-)tilting subcategories and (co)s…

Let $A$ be a finite dimensional algebra over an algebraically closed field $k$. Let $T$ be a tilting $A$-module and $B={\rm End}_A\ T$ be the endomorphism algebra of $T$. In this paper, we consider the correspondence between the tilting…

We give a reduction technique for silting intervals in extriangulated categories, which we call "silting interval reduction". It provides a reduction technique for tilting subcategories when the extriangulated categories are exact…

Let $A$ be a finite dimensional algebra over an algebraically closed field $k$, and $M$ be a partial tilting $A$-module. We prove that the Bongartz $\tau$-tilting complement of $M$ coincides with its Bongartz complement, and then we give a…

Initiated in work by Adachi, Iyama and Reiten, the area known as $\tau$-tilting theory plays a fundamental role in contemporary representation theory. In this paper we explore a higher-dimensional analogue of this theory, formulated with…

To a B-coring and a (B,A)-bimodule that is finitely generated and projective as a right A-module an A-coring is associated. This new coring is termed a base ring extension of a coring by a module. We study how the properties of a bimodule…

We discuss finiteness/infiniteness of $\tau$-tilting modules over tensor products of two symmetric algebras. As an application, we discuss that over block algebras of direct products of finite groups.

We explore some properties of wide subcategories of the category mod$\,(\Lambda)$ of finitely generated left $\Lambda$-modules, for some artin algebra $\Lambda.$ In particular we look at wide finitely generated subcategories and give a…

In this paper, we prove that relation-extensions of quasi-tilted algebras are 2-Calabi-Yau tilted. With the objective of describing the module category of a cluster-tilted algebra of euclidean type, we define the notion of reflection so…

In this note we give an overview of rigidity properties and Loewy lengths of tilting modules in the BGG category O associated to a reductive Lie algebra. These results are well-known by several specialists, but seem difficult to find in the…

In this paper, we classify certain subcategories of modules over a ring R. A wide subcategory of R-modules is an Abelian subcategory of R-Mod that is closed under extensions. We give a complete classification of wide subcategories of…

For any given symmetrizable Cartan matrix $C$ with a symmetrizer $D$, Gei\ss~ et al. (2016) introduced a generalized preprojective algebra $\Pi(C, D)$. We study tilting modules and support $\tau$-tilting modules for the generalized…

An extension $B\subset A$ of finite dimensional algebras is bounded if the $B$-$B$-bimodule $A/B$ is $B$-tensor nilpotent, its projective dimension is finite and $\mathrm{Tor}_i^B(A/B, (A/B)^{\otimes_B j})=0$ for all $i, j\geq 1$. We show…

$\tau$-tilting theory can be thought of as a generalization of the classical tilting theory which allows mutations at any indecomposable summand of a support $\tau$-tilting pair. Indeed, for any algebra $\Lambda$ its tilting modules…

Let $\C$ be a triangulated category with a cluster tilting subcategory $\T$. We introduce the notion of $\T[1]$-cluster tilting subcategories (also called ghost cluster tilting subcategories) of $\C$, which are a generalization of cluster…

In this paper, we study tau-tilting modules over Nakayama algebras. We establish bijections between tau-tilting modules, triangulations of a polygon with a puncture and certain integer sequences. Moreover, we give an algorithm to construct…

Holm (H. Holm, Modules with cosupport and injective functors, Algebr. Represent. Theor., 13 (2010), 543-560) considers categories of right modules dual to those with support in a set of finitely presented modules. We extend some of his…

In this paper, by using functor rings and functor categories, we study finiteness and purity of subcategories of the module categories. We give a characterisation of contravariantly finite resolving subcategories of the module category of…

Let $(\mathcal{B},\mathcal{A}, i, e, l)$ be a cleft extension of abelian categories. We prove that the functor $l$ preserves and reflects (Wakamatsu) tilting pairs of subcategories under certain conditions, unifying an abundance of known…

We investigate when the categories of all rational $A$-modules and of finite dimensional rational modules are closed under extensions inside the category of $C^*$-modules, where $C^*$ is the cofinite topological completion of $A$. We give a…

We build a bijection between the set $\sttilt\Lambda$ of isomorphism classes of basic support $\tau$-tilting modules over the Auslander algebra $\Lambda$ of $K[x]/(x^n)$ and the symmetric group $\mathfrak{S}_{n+1}$, which is an…