Horizontal and vertical mutation fans

  • Kiyoshi IgusaEmail author


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).


exceptional sequence m-cluster category semi-invariant pictures t-structures c-vectors g-vectors silting objects simple minded collections 


18E30 16G20 


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The author thanks the Chern Institute of Mathematics and organizers of the Workshop for their hospitality and the participants and referees for their inspiring comments.


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© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsBrandeis UniversityWalthamUSA

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