Related papers: A bijection between $m$-cluster-tilting objects an…
We classify the torsion pairs in a tube category and show that they are in bijection with maximal rigid objects in the extension of the tube category containing the Pruefer and adic modules. We show that the annulus geometric model for the…
Extriangulated categories give a simultaneous generalization of triangulated categories and exact categories. In this paper, we study silting subcategories of an extriangulated category. First, we show that a silting subcategory induces a…
In this article, we describe an explicit bijection between the set of $(m,n)$-words as defined by Pilaud and Poliakova and the set of of two-toned tilings of a strip of length $m+n$.
In this paper we introduce a new approach for organizing algebras of global dimension at most 2. We introduce the notion of cluster equivalence for these algebras, based on whether their generalized cluster categories are equivalent. We are…
An important result in tilting theory states that a class of modules over a ring is a tilting class if and only if it is the Ext-orthogonal class to a set of compact modules of bounded projective dimension. Moreover, cotilting classes are…
We extend so-called slit-slide-sew bijections to constellations and quasiconstellations. We present an involution on the set of hypermaps given with an orientation, one distinguished corner, and one distinguished edge leading away from the…
In this paper we present a bijection $\omega_n$ between two well known families of Catalan objects: the set of facets of the $m$-generalized cluster complex $\Delta^m(A_n)$ and the set of dominant regions in the $m$-Catalan arrangement…
We show how a cluster-tilted algebra of finite representation type is related to the corresponding tilted algebra, in the case of algebras defined over an algebraically closed field.
In this paper we give a geometric-combinatorial description of the cluster categories of type E. In particular, we give an explicit geometric description of all cluster tilting objects in the cluster category of type E_6. The model we…
We consider an orbit category of the bounded derived category of a path algebra of type A_n which can be viewed as a -(m+1)-cluster category, for m >= 1. In particular, we give a characterisation of those maximal m-rigid objects whose…
We study abelian localizations of triangulated categories induced by rigid contravariantly finite subcategories, and also triangulated structures on subfactor categories of triangulated categories. In this context we generalize recent…
We introduce the higher version of the notion of Adachi-Iyama-Reiten's support $\tau$-tilting pairs, which is a generalization of maximal $\tau_n$-rigid pairs in the sense of Jacobsen-J{\o}rgensen. Let $\mathcal C$ be an $(n+2)$-angulated…
In this paper the relationship between iterated tilted algebras and cluster-tilted algebras and relation-extensions is studied. In the Dynkin case, it is shown that the relationship is very strong and combinatorial.
We classify all finite dimensional algebras which are derived equivalent to m-cluster tilted algebras of type A.
Using cluster tilting theory, we investigate tilting objects in the stable category of vector bundles on a weighted projective line of weight type $(2, 2, 2, 2)$. More precisely, a tilting object consisting of rank-two bundles is…
In representation theory of algebras the notion of `mutation' often plays important roles, and two cases are well known, i.e. `cluster tilting mutation' and `exceptional mutation'. In this paper we focus on `tilting mutation', which has a…
Jasso-K\"{u}lshammer introduced the class of $d$-Nakayama algebras as a higher dimensional analogue of Nakayama algebras. In particular, they are endowed with a distinguished $d\mathbb{Z}$-cluster tilting subcategory. In this paper, we…
For any valued quiver, by using BGP-reflection functors, an injection from the set of preprojective objects in the cluster category to the set of cluster variables of the corresponding cluster algebra is given, the images are called…
We give a reduction technique for silting intervals in extriangulated categories, which we call "silting interval reduction". It provides a reduction technique for tilting subcategories when the extriangulated categories are exact…
We establish a bijection between rigged configurations and highest weight elements of a tensor product of Kirillov-Reshetikhin crystals for all nonexceptional types. A key idea for the proof is to embed both objects into bigger sets for…