Categorification of a frieze pattern determinant

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:119

Article

Baur, Karin¹  Marsh, Bethany Rose² 

[1] Graz Univ, Inst Math & Wissensch Rechnen, Heinrichstr 36, A-8010 Graz, Austria

[2] Univ Leeds, Sch Math, Leeds LS2 9JT, W Yorkshire, England

关键词: Determinant;    Minor;    Triangulation;    Polygon;    Derangement;    Cluster algebra;    Frieze pattern;    Root category;    Derived category;    Starting frame;   

DOI  :  10.1016/j.jcta.2012.02.006

来源: Elsevier

【 摘 要 】

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. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free