The interplay between 2-and-3-Calabi--Yau triangulated categories

Dong Yang

The interplay between 2-and-3-Calabi--Yau triangulated categories

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arxiv 1811.07553 v1 pith:XF5TUOXZ submitted 2018-11-19 math.RT math.AGmath.CT

Dong Yang This is my paper · ORCID

classification math.RTmath.AGmath.CT

keywords categoriestriangulatedcalabi--yaucluster-tiltingconstructionsobjectsamiotand-3-calabi--yau

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This short note surveys the constructions of 3-Calabi--Yau triangulated categories with simple-minded collections due to Ginzburg and Kontsevich--Soibelman and the constructions of 2-Calabi--Yau triangulated categories with cluster-tilting objects due to Buan--Marsh--Reineke--Reiten--Todorov and Amiot, and includes a discussion on the normal form of 2-Calabi--Yau triangulated categories with cluster-tilting objects.

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Quivers with potentials for Grassmannian cluster algebras
math.RT 2019-08 conditional novelty 6.0 of 10

For Grassmannian cluster algebras, the non-degenerate quiver with potential is rigid and unique up to right-equivalence, and the auto-equivalence group of its category matches the cluster automorphism group.

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