Horizontal and vertical mutation fans  

作　　者：Kiyoshi Igusa 

机构地区：[1]Department of Mathematics, Brandeis University

出　　处：《Science China Mathematics》2019年第7期1267-1288,共22页中国科学：数学（英文版）

摘　　要：We introduce diagrams for m-cluster categories which we call "horizontal" and "vertical" mutation fans. These are analogous to the mutation fans(also known as "semi-invariant pictures" or "scattering diagrams") for the standard(m = 1) cluster case, which are dual to the poset of finitely generated torsion classes. The purpose of these diagrams is to visualize mutations and analogues of maximal green sequences in the m-cluster category with special emphasis on the c-vectors(the "brick" labels).We introduce diagrams for m-cluster categories which we call "horizontal" and "vertical" mutation fans. These are analogous to the mutation fans(also known as "semi-invariant pictures" or "scattering diagrams") for the standard(m = 1) cluster case, which are dual to the poset of finitely generated torsion classes. The purpose of these diagrams is to visualize mutations and analogues of maximal green sequences in the m-cluster category with special emphasis on the c-vectors(the "brick" labels).

关 键 词：exceptional sequence m-cluster category SEMI-INVARIANT PICTURES t-structures c-vectors g-vectors silting objects simple minded COLLECTIONS 

分 类 号：O1[理学—数学]