相关论文: A geometric interpretation of the triangulated str…

The goals of this expository article are on one hand to describe how to construct ($m$-) cluster categories from triangulations (resp. from $m+2$-angulations) of polygons. On the other hand, we explain how to use translation quivers and…

We show that the $m$-cluster category of type $A_{n-1}$ is equivalent to a certain geometrically-defined category of diagonals of a regular $nm+2$-gon. This generalises a result of Caldero, Chapoton and Schiffler for $m=1$. The approach…

We show that the m-cluster category of type D_n is equivalent to a certain geometrically-defined category of arcs in a punctured regular nm-m+1-gon. This generalises a result of Schiffler for m=1. We use the notion of the mth power of a…

We first study the (canonical) orbit category of the bounded derived category of finite dimensional representations of a quiver with no infinite path, and we pay more attention on the case where the quiver is of infinite Dynkin type. In…

In this note we explain how to obtain cluster algebras from triangulations of (punctured) discs following the approach of S. Fomin, M. Shapiro and D. Thurston. Furthermore, we give a description of m-cluster categories via diagonals (arcs)…

We give a geometric realization of a subcategory of the $m$-cluster category $\mathcal{C}^m$ of type $\widetilde{A}_{p,q}$, by using $(m+2)$-angulations of an annulus with $p+q$ marked points. We also give a bijection between an equivalence…

We consider $m$-cluster tilted algebras arising from quivers of Euclidean type and we give necessary and sufficient conditions for those algebras to be representation finite. For the case $\widetilde{A}$, using the geometric realization, we…

We show that a subcategory of the $m$-cluster category of type $\tilde{D_n}$ is isomorphic to a category consisting of arcs in an $(n-2)m$-gon with two central $(m-1)$-gons inside of it. We show that the mutation of colored quivers and…

We give a geometric realization of module categories of type $\tilde{A}_n$. We work with oriented arcs to define a translation quiver isomorphic to the Auslander-Reiten quiver of the module category of type $\tilde{A}_n$. To get a…

We give a precise definition of folded quivers and folded cluster algebras. We give many examples of including some with finite mutation structure that do not have analogues in the unfolded cases. We relate these examples to the finite…

For the cluster category of a hereditary or a canonical algebra, equivalently for the cluster category of the hereditary category of coherent sheaves on a weighted projective line, we study the Grothendieck group with respect to an…

We consider triangulated orbit categories, with the motivating example of cluster categories, in their usual context of algebraic triangulated categories, then present them from another perspective in the framework of topological…

We use the maximal faces of the $m$-cluster complex of type A to describe the m-cluster tilted algebras of type A as quivers with relations. We then classify connected components of m-cluster tilted algebras of type A up to derived…

In a paper by Holm and Jorgensen, the cluster category $\mathscr{D}$ of type $A_\infty$, with Auslander-Reiten quiver $\mathbb{Z} A_\infty$, is introduced. Slices in the Auslander-Reiten quiver of $\mathscr{D}$ give rise to direct systems;…

This is a companion paper of arXiv:1901.09461, where different notions of dimension for triangulated categories are discussed. Here we compute dimensions for some examples of triangulated categories and thus illustrate and motivate material…

We give analogues of the Auslander correspondence for two classes of triangulated categories satisfying certain finiteness conditions. The first class is triangulated categories with additive generators and we consider their endomorphism…

We study in this paper the cluster category C(S,M) of a marked surface (S,M). We explicitly describe the objects in C(S,M) as direct sums of homotopy classes of curves in (S,M) and one-parameter families related to closed curves in (S,M).…

We study the cluster categories arising from marked surfaces (with punctures and non-empty boundaries). By constructing skewed-gentle algebras, we show that there is a bijection between tagged curves and string objects. Applications include…

In this article, we study the $(m+2)$-angulations on a Riemann surface, characterized with its boundary components, punctures, and gender. We count the number of arcs in such a surface, and associate a graded quiver with superpotential…

This is the first in a series of papers in which we study representations of the Brauer category and its allies. We define a general notion of triangular category that abstracts key properties of the triangular decomposition of a semisimple…