THE CLUSTER CATEGORY OF A CANONICAL ALGEBRA

By M. Barot, D. Kussin, H. Lenzing. 2008

63 citations recorded by the source corpus.

We study the cluster category of a canonical algebra A in terms of the hereditary category of coherent sheaves over the corresponding weighted projective line X. As an application we determine the automorphism group of the cluster category and show that the cluster-tilting objects form a cluster structure in the sense of Buan, Iyama, Reiten and Scott. The tilting graph of the sheaf category always coincides with the tilting or exchange graph of the cluster category. We show that this graph is connected if the Euler characteristic of X is non-negative, or equivalently, if A is of tame (domestic or tubular) representation type.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/49c392eedeb19cb7983b60ad19c4b5598a8a2c21

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Geometry and Topology

In Statistical and Nonlinear Physics

Citations in the corpus

Representations of Algebras and Related Topics (2011, background): “triangulated by [65] (the generalization from acyclic quivers to hereditary categories was ﬁrst suggested by Asashiba). These cluster categories are studied in details by Barot, Kussin and Lenzing in [16]. Recognition theorem for acyclic cluster categories. The following result due to Keller and Rei”
n-Abelian and n-exact categories (2014, background): “• Let C = CX be the cluster category associated with a weighted projective line, see [9] for details.”
Cluster categories (2010, background): “It has been shown in [11] that in the tubular case the cluster tilting graph is connected.”
Cluster structures from 2-Calabi–Yau categories with loops (2008, background): “The category CTn has also been studied in [2,3].”