Cluster algebras in algebraic lie theory

被引:0
作者
Ch. Geiss
B. Leclerc
J. Schröer
机构
[1] Instituto de Matemáticas Universidad Nacional Autónoma de México Ciudad Universitaria,
[2] LMNO UMR 6139 Université de Caen Basse-Normandie CNRS,undefined
[3] Mathematisches Institut Universität Bonn Endenicher Allee 60,undefined
来源
Transformation Groups | 2013年 / 18卷
关键词
Cluster Variable; Cluster Algebra; Coordinate Ring; Quantum Cluster; Preprojective Algebra;
D O I
暂无
中图分类号
学科分类号
摘要
We survey some recent constructions of cluster algebra structures on coordinate rings of unipotent subgroups and unipotent cells of Kac–Moody groups. We also review a quantized version of these results.
引用
收藏
页码:149 / 178
页数:29
相关论文
共 70 条
[1]  
Berenstein A(1996)Parametrizations of canonical bases and totally positive matrices Adv. Math. 122 49-149
[2]  
Fomin S(2005)Cluster algebras III: Upper bounds and double Bruhat cells Duke Math. J. 126 1-52
[3]  
Zelevinsky A(2005)Quantum cluster algebras Adv. Math. 195 405-455
[4]  
Berenstein A(2009)Cluster structures for 2-Calabi–Yau categories and unipotent groups Compos. Math. 145 1035-1079
[5]  
Fomin S(2011)Mutation of cluster-tilting objects and potentials Amer. J. Math. 133 835-887
[6]  
Zelevinsky A(2011)Total positivity criteria for partial flag varieties J. Algebra 348 402-415
[7]  
Berenstein A(2011)Categorification of skew-symmetrizable cluster algebras Alg. Represent. Theory 14 1087-1162
[8]  
Zelevinsky A(2008)Quivers with potentials and their representations I: Mutations Selecta Math. 14 59-119
[9]  
Buan A(2010)Quivers with potentials and their representations II: Applications to cluster algebras J. Amer. Math. Soc. 23 749-790
[10]  
Iyama O(1999)Double Bruhat cells and total positivity J. Amer. Math. Soc. 12 335-380