Related papers: $\tau$-tilting theory -- An introduction

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,…

We start with definitions of the general notions of the theory of $\Bbb Z_{2}$-graded algebras. Then we consider theory of inductive families of $\Bbb Z_{2}$-graded semisimple finite-dimensional algebras and its representations in the…

The aim of this note is to give a gentle introduction to algebras of partial triangulations of marked surfaces, following the structure of a talk given during the 49th symposium on ring theory and representation theory, held in Osaka. This…

These notes are our contribution to the Proceedings of the ICM 2026. We discuss some results we have obtained (in part jointly with coauthors) regarding the representation theory of reductive algebraic groups over algebraically closed…

We recall several results in Auslander-Reiten theory for finite-dimensional algebras over fields and orders over complete local rings. Then we introduce $n$-cluster tilting subcategories and higher theory of almost split sequences and…

The notion of the flow introduced by Kitaev is a manifestly topological formulation of the winding number on a real lattice. First, we show in this paper that the flow is quite useful for practical numerical computations for systems without…

We show that certain tilting results for quivers are formal consequences of stability, and as such are part of a formal calculus available in any abstract stable homotopy theory. Thus these results are for example valid over arbitrary…

In this paper we introduce, according to one of the main ideas of $\tau$-tilting theory, the $\tau$-Hochschild cohomology in degree one of a finite dimensional $k$-algebra $\Lambda$, where $k$ is a field. We define the excess of $\Lambda$…

The purpose of this note is to provide a short invitation to the universal algebraic approach to topological string theory. In the first section we make an attempt to explain the origin of this approach and how it fits into the bigger…

We introduce the notion of n-representation-finiteness, generalizing representation-finite hereditary algebras. We establish the procedure of n-APR tilting, and show that it preserves n-representation-finiteness. We give some combinatorial…

Inspired by the work of Wang and Zhou [4] for Rota-Baxter algebras, we develop a cohomology theory of Rota-Baxter systems and justify it by interpreting the lower degree cohomology groups as formal deformations and as abelian extensions of…

If (A,B) and (A',B') are co-t-structures of a triangulated category, then (A',B') is called intermediate if A \subseteq A' \subseteq \Sigma A. Our main results show that intermediate co-t-structures are in bijection with two-term silting…

The aim of this paper is to study a poset isomorphism between two support $\tau$-tilting posets. We take several algebraic information from combinatorial properties of support $\tau$-tilting posets. As an application, we treat a certain…

Let $K:k$ be a field extension and let $\Lambda$ be a finite-dimensional $k$-algebra. We investigate the relationship between $\Lambda$ and $\Lambda_K = \Lambda \otimes_k K$ with particular emphasis on various aspects of $\tau$-tilting…

We prove that a finite dimensional algebra $\Lambda$ is $\tau-$tilting finite if and only if all the bricks over $\Lambda$ are finitely generated. This is obtained as a consequence of the existence of proper locally maximal torsion classes…

In this article we study support $\tau$-tilting modules, semibricks and more over blocks of group algebras. Let $k$ be an algebraically closed field of characteristic $p>0$, $\tilde{G}$ a finite group and $G$ a normal subgroup of…

We study support $\tau$-tilting modules over preprojective algebras of Dynkin type. We classify basic support $\tau$-tilting modules by giving a bijection with elements in the corresponding Weyl groups. Moreover we show that they are in…

Let $B$ be the one-point extension algebra of $A$ by an $A$-module $X$. We proved that every support $\tau$-tilting $A$-module can be extended to be a support $\tau$-tilting $B$-module by two different ways. As a consequence, it is shown…

Let $\mathcal{D}$ be a Hom-finite, Krull-Schmidt, 2-Calabi-Yau triangulated category with a rigid object $R$. Let $\Lambda=\operatorname{End}_{\mathcal{D}}R$ be the endomorphism algebra of $R$. We introduce the notion of mutation of maximal…

We observe that over an algebraically closed field, any finite-dimensional algebra is the endomorphism algebra of an m-cluster-tilting object in a triangulated m-Calabi-Yau category, where m is any integer greater than 2.