相关论文: Derived equivalence classification for cluster-til…
Cluster algebras are a class of commutative algebras whose generators are defined by a recursive process called mutation. We give a brief introduction to cluster algebras, and explain how discrete integrable systems can appear in the…
In the derived category of mod-KQ for Dynkin quiver Q, we construct a full subcategory in a canonical way, so that its endomorphism algebra is a higher Auslander algebra of global dimension $3k+2$ for any $k\geq 1$. Furthermore, we extend…
In this paper we first study clusters in type $\tilde{\mathbb{A}}$ by collecting them into a finite number of infinite families given by Dehn twists of their corresponding triangulations, and show that these families are counted by the…
We prove that any derived equivalence between derived-discrete algebras of finite global dimension is standard, that is, isomorphic to the derived tensor functor by a two-sided tilting complex.
In this paper, we will place clusters in type $\tilde{\mathbb{A}}$ (equivalently triangluations of an annulus) into infinite families parametrized by winding numbers of certain arcs in the corresponding triangulation. We will count how many…
We give an introduction to the theory of cluster categories and cluster tilted algebras. We include some background on the theory of cluster algebras, and discuss the interplay with cluster categories and cluster tilted algebras.
We characterize the indecomposable transjective modules over an arbitrary cluster-tilted algebra that do not lie on a local slice, and we provide a sharp upper bound for the number of (isoclasses of) these modules.
In this paper we define the modified Ringel-Hall algebra $\cm\ch(\ca)$ of a hereditary abelian category $\ca$ from the category $C^b(\mathcal{A})$ of bounded $\mathbb{Z}$-graded complexes. Two main results have been obtained. One is to give…
For any positive integer $n$, $n$-derived-simple derived discrete algebras are classified up to derived equivalence. Furthermore, the Jordan-H\"older theorems for all kinds of derived categories of derived discrete algebras are obtained.
The classification of Grassmannian cluster algebras resembles that of regular polygonal tilings. We conjecture that this resemblance may indicate a deeper connection between these seemingly unrelated structures.
In this paper we discuss, in terms of quivers with relations, sufficient and necessary conditions for an algebra to be a quasitilted algebra. We start with an algebra with global dimension two and we give a sufficient condition for it to be…
Let D be a triangulated category with a cluster tilting subcategory U. The quotient category D/U is abelian; suppose that it has finite global dimension. We show that projection from D to D/U sends cluster tilting subcategories of D to…
Let A be a path A-infinity-algebra over a positively graded quiver Q. It is proved that the derived category of A is triangulated equivalent to the derived category of kQ, which is viewed as a dg algebra with trivial differential. The main…
We calculate the cluster modular groups of affine and doubly extended typecluster algebras in a uniform way by introducing a new family of quivers. We use this uniformdescription to construct a natural finite quotient of the cluster complex…
A twisting system is one of the major tools to study graded algebras, however, it is often difficult to construct a (non-algebraic) twisting system if a graded algebra is given by generators and relations. In this paper, we show that a…
In this paper we determine the derived representation type of quadratic string algebras and we prove that every derived tame quadratic string algebra whose quiver has cycles is derived equivalent to some skewed-gentle algebra.
Motivated by the problem of classifying quantum symmetries of non-semisimple, finite-dimensional associative algebras, we define a notion of connection between bounded quivers and build a bicategory of bounded quivers and quiver…
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…
We construct an equivalence between the derived category of sheaves on an elliptic threefold without a section and a derived category of twisted sheaves (modules over an Azumaya algebra) on any small resolution of its relative Jacobian.
Let C be the category of finite-dimensional representations of a quantum affine algebra of simply-laced type. We introduce certain monoidal subcategories C_l (l integer) of C and we study their Grothendieck rings using cluster algebras.