2023/11/11 by Bernhard Keller, Junyang Liu, Keller, Bernhard +1 · 4 citations
Mathematics · #16E35 #18G80 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Representation Theory (math.RT) #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2311.06538
openalex publication_date 2023/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a survey paper in 2011, Amiot proposed a conjectural characterisation of the cluster categories which were conceived in the mid 2000s to lift the combinatorics of Fomin-Zelevinsky's cluster algebras to the categorical level. This paper is devoted to a proof of (a variant of) her conjecture. More generally, cluster categories admit higher-dimensional and relative variants, the so-called Higgs categories recently introduced by Wu. We also prove higher-dimensional and relative variants of the conjecture.