A MODULE-THEORETIC INTERPRETATION OF SCHIFFLER'S EXPANSION FORMULA

被引：2

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

共 12 条

[1]

Bennis D, 2010, INT ELECTRON J ALGEB, V8, P30

[2] FIRST, SECOND, AND THIRD CHANGE OF RINGS THEOREMS FOR GORENSTEIN HOMOLOGICAL DIMENSIONS [J].

Bennis, Driss ;

Mahdou, Najib .

COMMUNICATIONS IN ALGEBRA, 2010, 38 (10) :3837-3850

[3] RINGS OVER WHICH ALL MODULES ARE STRONGLY GORENSTEIN PROJECTIVE [J].

Bennis, Driss ;

Mahdou, Najib ;

Ouarghi, Khalid .

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2010, 40 (03) :749-759

[4]

Bennis D, 2010, P AM MATH SOC, V138, P461

[5]

Fuchs L., 2001, MODULES NONNOETHERIA

[6] INTEGRAL DOMAINS IN WHICH EACH NON-ZERO IDEAL IS DIVISORIAL [J].

HEINZER, W .

MATHEMATIKA, 1968, 15 (30P2) :164-&

[7] Gorenstein homological dimensions [J].

Holm, H .

JOURNAL OF PURE AND APPLIED ALGEBRA, 2004, 189 (1-3) :167-193

[8]

Kaplansky I., 1974, Commutative Rings

[9] On (Strongly) Gorenstein (Semi)Hereditary Rings [J].

Mahdou, Najib ;

Tamekkante, Mohammed .

ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING, 2011, 36 (03) :431-440

[10]

Rotman JJ, 2009, UNIVERSITEXT, P1, DOI 10.1007/978-0-387-68324-9_1

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