English

Horizontal and vertical mutation fans

Representation Theory 2018-05-18 v2

Abstract

We introduce diagrams for mm-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=1m=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 mm-cluster category with special emphasis on the cc-vectors (the "brick" labels).

Cite

@article{arxiv.1805.04799,
  title  = {Horizontal and vertical mutation fans},
  author = {Kiyoshi Igusa},
  journal= {arXiv preprint arXiv:1805.04799},
  year   = {2018}
}

Comments

23 pages, 10 figures, presented at Workshop on Cluster Algebras and Related Topics held at the Chern Institute of Mathematics, Nankai University, China, July 10-13, 2017, accepted for publication in SCIENCE CHINA Mathematics, v2: minor corrections

R2 v1 2026-06-23T01:53:04.697Z