F-Matrices of Cluster Algebras from Triangulated Surfaces

被引：2

作者：

Gyoda, Yasuaki ^{[1
]}

Yurikusa, Toshiya ^{[2
]}

机构：

[1] Nagoya Univ, Grad Sch Math, Chikusa Ku, Nagoya, Aichi 4648602, Japan

[2] Tohoku Univ, Math Inst, Aoba Ku, Sendai, Miyagi 9808578, Japan

来源：

ANNALS OF COMBINATORICS | 2020年 / 24卷 / 04期

关键词：

Marked surface; Tagged triangulation; Intersection number; Cluster algebra; F-matrix; QUIVERS; BASES;

D O I：

10.1007/s00026-020-00507-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For a given marked surface (S, M) and a fixed tagged triangulation T of (S, M), we show that each tagged triangulation T' of (S, M) is uniquely determined by the intersection numbers of tagged arcs of T and tagged arcs of T'. As a consequence, each cluster in the cluster algebra A(T) is uniquely determined by its F-matrix which is a new numerical invariant of the cluster introduced by Fujiwara and Gyoda.

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收藏

页码：649 / 695

页数：47

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