Related papers: Mutating ordered $\tau$-rigid modules with applica…

We introduce a notion of mutation for $\tau$-exceptional sequences of modules over arbitrary finite dimensional algebras. For hereditary algebras, we show that this coincides with the classical mutation of exceptional sequences. For rank…

We establish some properties of $\tau$-exceptional sequences for finite-dimensional algebras. In an earlier paper we established a bijection between the set of ordered support $\tau$-tilting modules and the set of complete signed…

We prove that mutation of complete $\tau$-exceptional sequences is transitive for $\tau$-tilting finite algebras.

We study universal localisations, in the sense of Cohn and Schofield, for finite dimensional algebras and classify them by certain subcategories of our initial module category. A complete classification is presented in the hereditary case…

We characterise those basic and connected Nakayama algebras $\Lambda$ for which the mutation of $\tau$-exceptional sequences respects the braid group relations. We show that this is the case if and only if $\Lambda$ is hereditary or all…

In this paper, we show that for an algebra $\Lambda$ with radical square zero and an indecomposable $\Lambda$-module $M$ such that $\Lambda$ is Gorenstein of finite type or $\tau M$ is $\tau$-rigid, $M$ is $\tau$-rigid if and only if the…

Mutation of {\tau}-tilting modules is a basic operation to construct a new support {\tau}-tilting module from a given one by replacing a direct summand. The aim of this paper is to give a positive answer to the question posed in [AIR,…

The class of support $\tau$-tilting modules was introduced recently by Adachi, Iyama and Reiten. These modules complete the class of tilting modules from the point of view of mutations. Given a finite dimensional algebra $A$, we study all…

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…

The class of support $\tau$-tilting modules was introduced to provide a completion of the class of tilting modules from the point of view of mutations. In this article we study $\tau$-tilting finite algebras, i.e. finite dimensional…

For $\mathcal{A}_t$, the Auslander algebra of $K[x]/(x^t)$, it is shown that every complete exceptional sequence of $\mathcal{A}_t$-modules is a complete $\tau$-exceptional sequence. Moreover, it is established that the mutation of complete…

Support $\tau$-tilting pairs, functorially finite torsion classes and $2$-term silting complexes are three much studied concepts in the representation theory of finite-dimensional algebras, which moreover turn out to be connected via work…

Let $\Lambda$ be a finite-dimensional basic algebra. Sakai recently used certain sequences of image-cokernel-extension-closed (ICE-closed) subcategories of finitely generated $\Lambda$-modules to classify certain (generalized) intermediate…

Nakayama automorphisms play an important role in several mathematical branches, which are known to be tough to compute in general. We compute the Nakayama automorphism $\nu$ of any Ore extension $R[x; \sigma, \delta]$ over a polynomial…

$\tau$-rigid modules are essential in the $\tau$-tilting theory introduced by Adachi, Iyama and Reiten. In this paper, we give equivalent conditions for Iwanaga-Gorenstein algebras with self-injective dimension at most one in terms of…

Buan, Iyama, Reiten and Smith proved that cluster-tilting objects in triangulated 2-Calabi--Yau categories are closely connected with mutation of quivers with potentials over an algebraically closed field. We prove a more general statement…

In the representation theory of finite-dimensional algebras, the study of projective presentations of maximal rank is closely related to the study of generically $\tau$-regular irreducible components of varieties of modules over such…

We give a characterization of $\tau$-rigid modules over Auslander algebras in terms of projective dimension of modules. Moreover, we show that for an Auslander algebra $\Lambda$ admitting finite number of non-isomorphic basic tilting…

For a hereditary, finite-dimensional algebra $A$ the Coxeter transformation extends the action of the Auslander--Reiten translation on the non-projective indecomposable modules to a linear endomorphism of the Grothendieck group of the…

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…