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On Amiot's conjecture

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arxiv 2311.06538 v3 pith:K4UU6K4M submitted 2023-11-11 math.RT math.ACmath.AGmath.KTmath.SG

Bernhard Keller , Junyang Liu This is my paper · ORCID
classification math.RTmath.ACmath.AGmath.KTmath.SG
keywords categoriesclusterconjectureamiothigher-dimensionalrelativevariantsadmit
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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.

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Cited by 1 Pith paper

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  1. The Derived Auslander--Iyama Correspondence II: Bimodule Calabi--Yau Structures

    math.RT 2025-09 conditional novelty 7.0 of 10

    The Auslander-Iyama correspondence is extended to bimodule right Calabi-Yau dg algebras via a new Massey bimodule cohomology, with an obstruction (BV operator on universal Massey product) and a first non-liftable example.

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