2017/06/20 by Lucie Jacquet-Malo, Jacquet-Malo, Lucie · 3 citations
Mathematics · #05C62 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Arc (geometry) #Bijection #Bijection, injection and surjection #Category Theory (math.CT) #Cluster (spacecraft) #Combinatorics #Computer science #FOS: Mathematics #Geology #Geometry #Mathematics #Primary: 18E30 #Pure mathematics #Representation Theory (math.RT) #Secondary: 13F60 #Type (biology) #math.CT #math.RT #msc:05C62 #msc:13F60 #msc:18E30
paper · pdf · doi:10.48550/arxiv.1706.06866
35 pages
openalex publication_date 2017/06/20 · arxiv created 2021/09/20 · arxiv updated 2021/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this article, we study the geometric realizations of m-cluster categories of Dynkin types A, D, A and D. We show, in those four cases, that there is a bijection between (m+2)-angulations and isoclasses of basic m-cluster tilting objects. Under these bijections, flips of (m+2)-angulations correspond to mutations of m-cluster tilting objects. Our strategy consists in showing that certain Iyama-Yoshino reductions of the m-cluster categories under consideration can be described in terms of cutting along an arc the corresponding geometric realizations. This allows to infer results from small cases to the general ones.