Categorification of a frieze pattern determinant
Karin Baur, Bethany Marsh
TL;DR
This paper generalizes the determinant calculation of matrices from Conway-Coxeter frieze patterns to cluster variables in type A cluster algebras, providing a representation-theoretic interpretation.
Contribution
It extends the determinant formula to cluster algebra frieze patterns and links it to indecomposable objects in the root category of type A.
Findings
Determinant formula for cluster algebra frieze patterns
Representation-theoretic interpretation in root categories
Generalization of previous combinatorial results
Abstract
Broline, Crowe and Isaacs have computed the determinant of a matrix associated to a Conway-Coxeter frieze pattern. We generalise their result to the corresponding frieze pattern of cluster variables arising from the Fomin-Zelevinsky cluster algebra of type A. We give a representation-theoretic interpretation of this result in terms of certain configurations of indecomposable objects in the root category of type A.
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