Geometric construction of cluster algebras and cluster categories
Karin Baur
TL;DR
This paper explores geometric methods to construct cluster algebras from triangulated punctured discs and describes m-cluster categories using diagonals in polygons and powers of translation quivers, linking geometry and algebra.
Contribution
It introduces a geometric approach to derive cluster algebras from triangulations and characterizes m-cluster categories through diagonals and translation quivers, extending prior algebraic frameworks.
Findings
Cluster algebras can be obtained from triangulations of punctured discs.
m-cluster categories are described via diagonals in polygons.
m-cluster categories are also characterized using powers of translation quivers.
Abstract
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) in (punctured) polygons and of m-cluster categories via powers of translation quivers as given in joint work with R. Marsh.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology