A MODULE-THEORETIC INTERPRETATION OF SCHIFFLER'S EXPANSION FORMULA

被引：1

作者：

Bruestle, Thomas ^{[1
]}

Zhang, Jie ^{[2
]}

机构：

[1] Univ Sherbrooke, Dept Math, Sherbrooke, PQ J1K 2R1, Canada

[2] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China

来源：

COMMUNICATIONS IN ALGEBRA | 2013年 / 41卷 / 01期

关键词：

Cluster algebras; Cluster categories; Marked surfaces; Representations; GORENSTEIN HOMOLOGICAL DIMENSIONS; RINGS;

D O I：

10.1080/00927872.2011.629267

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a module-theoretic interpretation of Schiffler's expansion formula which is defined combinatorially in terms of complete (Gamma, gamma)-paths in order to get the expansion of the cluster variables in the cluster algebra of a marked surface (S, M). Based on the geometric description of the indecomposable objects of the cluster category of the marked surface (S, M), we show the coincidence of Schiffler-Thomas' expansion formula and the cluster character defined by Palu.

引用

页码：260 / 283

页数：24