A Caldero-Chapoton formula for generalized Cluster Categories
Salom\'on Dominguez, Christof Geiss
TL;DR
This paper extends the Caldero-Chapoton formula to generalized cluster categories with cluster tilting objects by utilizing Auslander-Reiten triangles, broadening its applicability beyond hereditary algebras of Dynkin type.
Contribution
It introduces a generalized Caldero-Chapoton formula for cluster categories with cluster tilting objects using Auslander-Reiten triangles, expanding previous hereditary algebra results.
Findings
Extended Caldero-Chapoton formula to generalized cluster categories
Connected cluster characters via Auslander-Reiten triangles
Broadened understanding of cluster algebra structures
Abstract
The Caldero-Chapoton formula relates for hereditary algebras of Dynkin type the cluster characters of the end terms of an Auslander-Reiten sequence with the cluster character of the middle term. We extend this result to generalized cluster categories with cluster tilting object by considering Auslander-Reiten triangles.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology