A = u for Locally Acyclic Cluster Algebras

被引：24
作者：
Muller, Greg [1 ]
机构：
[1] Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA
来源：
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2014年 / 10卷
基金：
美国国家科学基金会;
关键词：
cluster algebras; upper cluster algebras; acyclic cluster algebras;
D O I：
10.3842/SIGMA.2014.094
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This note presents a self-contained proof that acyclic and locally acyclic cluster algebras coincide with their upper cluster algebras.
引用
收藏
页数：8
相关论文
共 12 条
[1]  
[Anonymous], 2010, Mathematical Surveys and Monographs
[2]   Cluster algebras III: Upper bounds and double Bruhat cells [J].
Berenstein, A ;
Fomin, S ;
Zelevinsky, A .
DUKE MATHEMATICAL JOURNAL, 2005, 126 (01) :1-52
[3]   Moduli spaces of local systems and higher teichmuller theory [J].
Fock, Vladimir ;
Goncharov, Alexander .
PUBLICATIONS MATHEMATIQUES DE L'IHES NO 103, 2006, 103 (1) :1-211
[4]   Cluster algebras I: Foundations [J].
Fomin, S ;
Zelevinsky, A .
JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2002, 15 (02) :497-529
[5]  
Fomin S., 2003, CLUSTER ALGEBRAS NOT, P1
[6]   Cluster algebras and triangulated surfaces. Part I: Cluster complexes [J].
Fomin, Sergey ;
Shapiro, Michael ;
Thurston, Dylan .
ACTA MATHEMATICA, 2008, 201 (01) :83-146
[7]   Cluster algebras IV: Coefficients [J].
Fomin, Sergey ;
Zelevinsky, Andrei .
COMPOSITIO MATHEMATICA, 2007, 143 (01) :112-164
[8]   Cluster algebras and Weil-Petersson forms [J].
Gekhtman, M ;
Shapiro, M ;
Vainshtein, A .
DUKE MATHEMATICAL JOURNAL, 2005, 127 (02) :291-311
[9]  
Keller B, 2011, B IRAN MATH SOC, V37, P187
[10]  
Matherne J., INT MATH RE IN PRESS
12