Related papers: $n$-term silting complexes in $K^b(proj(\Lambda))$

We study the class of modules, called cosilting modules, which are defined as the categorical duals of silting module. Several characterizations of these modules and connections with silting modules are presented. We prove that Bazzoni…

We construct a new class of symmetric algebras of tame representation type that are also the endomorphism algebras of cluster tilting objects in 2-Calabi-Yau triangulated categories, hence all their non-projective indecomposable modules are…

Let $\mathbb{Z}$ be the integer numbers, $\mathbb{K}$ an algebraically closed field, $\Lambda$ a finite dimensional $\mathbb{K}$-algebra, mod$\Lambda$ the category of finitely generated right modules, proj$\Lambda$ the full subcategory of…

We construct via usual graph theory a class of associative dialgebras as well as a class of coassociative L-coalgebras. Tiling of the (n^2,1)-De bruijn graphs are also obtained and constructions of cubical trialgebras, (notion defined by…

In this paper, motivated by a $\tau$-tilting version of the Brauer-Thrall Conjectures, we study general properties of band modules and their endomorphisms in the module category of a finite dimensional algebra. As an application we describe…

As a generalization of acyclic 2-Calabi-Yau categories, we consider 2-Calabi-Yau categories with a directed cluster-tilting subcategory; we study their cluster-tilting subcategories and the cluster combinatorics that they encode. We show…

We show that the category of projective modules over a graded commutative ring admits a triangulation with respect to module suspension if and only if the ring is a finite product of graded fields and exterior algebras on one generator over…

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…

The main result of this paper is that there is sometimes a triangulated equivalence between $D_Q( A )$, the $Q$-shaped derived category of an algebra $A$, and $D( B )$, the classic derived category of a different algebra $B$. By…

It is well known that for Auslander algebras, the category of all (finitely generated) projective modules is an abelian category and this property of abelianness characterizes Auslander algebras by Tachikawa theorem in 1974. Let $n$ be a…

Let $\mathcal C$ be a Krull-Schmidt triangulated category with shift functor $[1]$ and $\mathcal R$ be a rigid subcategory of $\mathcal C$. We are concerned with the mutation of two-term weak $\mathcal R[1]$-cluster tilting subcategories.…

We show that there is a special bijection between the indecomposable summands of the two modules which form a basic support $\tau$--tilting pair and the indecomposable summands of the two modules which form another basic support…

For a given cluster-tilted algebra $A$ of tame type, it is proved that different indecomposable $\tau$-rigid $A$-modules have different dimension vectors. This is motivated by Fomin-Zelevinsky's denominator conjecture for cluster algebras.…

Higher homological algebra was introduced by Iyama. It is also known as $n$-homological algebra where $n \geq 2$ is a fixed integer, and it deals with $n$-cluster tilting subcategories of abelian categories. All short exact sequences in…

This paper investigates finiteness conditions for gentle and skew-gentle algebras. First, we prove that a skew-gentle algebra is $\tau$-tilting finite if and only if it is representation-finite, which extends the result for gentle algebras…

Let $\mathcal{P}^{<\infty} (\Lambda$-mod$)$ be the category of finitely generated left modules of finite projective dimension over a basic Artin algebra $\Lambda$. We develop an applicable criterion that reduces the test for contravariant…

In this paper we investigate the endomorphism algebras of standard cluster tilting objects in the stably 2-Calabi-Yau categories $\Sub{\Lambda_w}$ with elements $w$ in Coxeter groups in \cite{BIRSc}. They are examples of the 2-Auslander…

It is demonstrated that any almost-tilting module over a gentle algebra is indeed partial-tilting, meaning it can be completed as a tilting module. Furthermore, such a module has at most $2n$ possible complements, thereby confirming a…

In this paper, we introduce the notion of $\nu$-stable silting-discrete algebras, which unify silting-discrete algebras and tilting-discrete self-injective algebras, where $\nu$ is a triangle auto-equivalence of the bounded homotopy…

Inspired by the tropical duality in cluster algebras, we introduce c-vectors for finite-dimensional algebras via $\tau$-tilting theory. Let $A$ be a finite-dimensional algebra over a field $k$. Each c-vector of $A$ can be realized as the…