Horizontal and vertical mutation fans

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2019,（7）
• 页码范围: 1267-1288
• 页数: 22页
• 语种: 英文

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).