Linear independence of cluster monomials for skew-symmetric cluster algebras

被引：41

作者：

Irelli, Giovanni Cerulli ^{[1
]}

Keller, Bernhard ^{[2
]}

Labardini-Fragoso, Daniel ^{[1
]}

Plamondon, Pierre-Guy ^{[3
]}

机构：

[1] Univ Bonn, Math Inst, D-53115 Bonn, Germany

[2] Univ Paris 07, UFR Math, F-75205 Paris 13, France

[3] Univ Caen, Equipe Algebre Geometrie & Log, Lab LMNO, F-14032 Caen, France

来源：

COMPOSITIO MATHEMATICA | 2013年 / 149卷 / 10期

关键词：

cluster algebras; cluster categories; cluster monomials; TRIANGULATED CATEGORIES; QUIVERS; POTENTIALS; BASES;

D O I：

10.1112/S0010437X1300732X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Fomin-Zelevinsky conjectured that in any cluster algebra, the cluster monomials are linearly independent and that the exchange graph and cluster complex are independent of the choice of coefficients. We confirm these conjectures for all skew-symmetric cluster algebras.

引用

页码：1753 / 1764

页数：12

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