Related papers: Cluster categories for topologists
The paper describes and classifies hexagonal circular 3-webs on unit sphere such that the polar points of the web circles lie on a twisted cubic, thus completing classification of hexagonal circular 3-webs with algebraic polar curves of…
Cluster ensemble is a pair of positive spaces (X, A) related by a map p: A -> X. It generalizes cluster algebras of Fomin and Zelevinsky, which are related to the A-space. We develope general properties of cluster ensembles, including its…
We show that the cellular objects in the module category over a motivic E infinity ring spectrum E can be described as the module category over a graded topological spectrum if E is strongly periodizable in our language. A similar statement…
Arbitrarily many pairwise inequivalent modular categories can share the same modular data. We exhibit a family of examples that are module categories over twisted Drinfeld doubles of finite groups, and thus in particular integral modular…
We classify elements of a cluster modular group into three types. We characterize them in terms of fixed point property of the action on the tropical compactifications associated with the corresponding cluster ensemble. The characterization…
Clustering is an unsupervised learning problem that aims to partition unlabelled data points into groups with similar features. Traditional clustering algorithms provide limited insight into the groups they find as their main focus is…
Restriction categories were established to handle maps that are partially defined with respect to composition. Tensor topology realises that monoidal categories have an intrinsic notion of space, and deals with objects and maps that are…
Given an essentially small triangulated category it is possible to give a metric on it, to complete it with respect to the metric, and to look at the subcategory of objects in the completion which are compactly supported with respect to the…
Hom- and Riedtmann configurations were studied in the context of stable module categories of selfinjective algebras and a certain orbit category C of the bounded derived category of a Dynkin quiver, which is highly reminiscent of the…
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…
Let $\mathcal{C}$ be a Hom-finite triangulated 2-Calabi-Yau category with a cluster tilting object. Under some constructibility assumptions on $\mathcal{C}$ which are satisfied for instance by cluster categories, by generalized cluster…
Acyclic cluster algebras have an interpretation in terms of tilting objects in a Calabi-Yau category defined by some hereditary algebra. For a given quiver $Q$ it is thus desirable to decide if the cluster algebra defined by $Q$ is acyclic.…
The notion of a pseudo cluster tilting subcategory $\mathcal X$ in an extriangulated category $\mathcal C$ is defined in this article. We prove that the quotient category $\mathcal C/\mathcal X$, obtained by factoring an extriangulated…
We consider clustering in group decision making where the opinions are given by pairwise comparison matrices. In particular, the k-medoids model is suggested to classify the matrices since it has a linear programming problem formulation…
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…
Cluster categories have been introduced by Buan, Marsh, Reineke, Reiten and Todorov in order to categorify Fomin-Zelevinsky cluster algebras. This survey motivates and outlines the construction of a generalization of cluster categories, and…
For each positive integer $n$ we introduce the notion of $n$-exangulated categories as higher dimensional analogues of extriangulated categories defined by Nakaoka-Palu. We characterize which $n$-exangulated categories are $n$-exact in the…
This is a first step guide to the theory of cluster algebras. We especially focus on basic notions, techniques, and results concerning seeds, cluster patterns, and cluster algebras.
The cluster soft point is an attempt to introduce a novel generalization of the soft closure point and the soft limit point. A cluster soft set is defined to be the system of all cluster soft points of a soft set. Then the fundamental…
Many clustering schemes are defined by optimizing an objective function defined on the partitions of the underlying set of a finite metric space. In this paper, we construct a framework for studying what happens when we instead impose…