Related papers: Tilting quivers for BB-tilted algebras

Inspired by tau-tilting theory [AIR], we introduce the notion of nu-stable support tau-tilting modules. For any finite dimensional selfinjective algebra {\Lambda}, we give bijections between two-term tilting complexes in Kb(proj {\Lambda}),…

Given a simple finite-dimensional Lie algebra and an automorphism of finite order, one defines the notion of a twisted toroidal Lie algebra. In this paper, we construct representations of twisted toroidal Lie algebras from twisted modules…

Given a finite dimensional algebra $C$ (over an algebraically closed field) of global dimension at most two, we define its relation-extension algebra to be the trivial extension $C\ltimes \Ext_C^2(DC,C)$ of $C$ by the $C$-$C$-bimodule…

In association with a finite dimensional algebra A of global dimension two, we consider the endomorphism algebra of A, viewed as an object in the triangulated hull of the orbit category of the bounded derived category, in the sense of…

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…

We study the module categories of a tilted algebra C and the corresponding cluster-tilted algebra B. In particular, we study which $\tau$-rigid C-modules are also $\tau$-rigid B-modules.

We develop a structure theory for two classes of infinite dimensional modules over tame hereditary algebras: the Baer modules, and the Mittag-Leffler ones.

In this work we study the connection between iterated tilted algebras and m-cluster tilted algebras. We show that an iterated tilted algebra induces an m-cluster tilted algebra. This m-cluster tilted algebra can be seen as a trivial…

Let $B$ be an one-point extension of a finite dimensional $k$-algebra $A$ by a simple $A$-module at a source point $i$. In this paper, we classify the $\tau$-tilting modules over $B$. Moreover, it is shown that there are equations $$|\tilt…

We give an explicit description of the mutation classes of quivers of type \tilde{A}_n. Furthermore, we provide a complete classification of cluster tilted algebras of type \tilde{A}_n up to derived equivalence. We show that the bounded…

Let $A$ be a hereditary algebra. We construct a fundamental domain for the cluster category of $A$ inside the category of modules over the duplicated algebra $\bar{A}$ of $A$. We then prove that there exists a bijection between the tilting…

In this paper, we characterize all the finite dimensional algebras that are m-cluster tilted algebras of type A tilde. We show that these algebras are gentle and we give an explicit description of their quivers with relations.

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…

Let $\Field$ be an algebraically closed field. For $n \in \mathbb{N}$ and $\delta, \delta_L, \delta_R, \kappa_L, \kappa_R, \kappa \in \Field$, the symplectic blob algebra $\sba(\delta, \delta_L, \delta_R, \kappa_L, \kappa_R, \kappa)$ is a…

Let $A$ be a quasi-hereditary algebra. We prove that in many cases, a tilting module is rigid (i.e. has identical radical and socle series) if it does not have certain subquotients whose composition factors extend more than one layer in the…

We define an operation which associates to a pair (B,M) where B is a cluster-tilted algebra and M is a B-module which lies in a local slice of B, a new cluster-tilted algebra B'. In terms of the quivers, this operation corresponds to adding…

We use the category of linear complexes of tilting modules for the BGG category O, associated with a semi-simple complex finite-dimensional Lie algebra g, to reprove in purely algebraic way several known results about O obtained earlier by…

Given a finite acyclic quiver Q with path algebra kQ, Ingalls and Thomas have exhibited a bijection between the set of Morita equivalence classes of support-tilting modules and the set of thick subcategories of mod kQ and they have…

We explicitly construct two-sided tilting complexes corresponding to Membrillo-Hern\'{a}ndez's tree-to-star tilting complexes for generalized Brauer tree algebras.

We give a complete description of all special biserial cluster-tilted algebras over a finite dimensional hereditary algebra H over an algebraically closed field K.