Lattices of t-structures and thick subcategories for discrete cluster categories

Sira Gratz; Alexandra Zvonareva

doi:10.1112/jlms.12705

Lattices of t-structures and thick subcategories for discrete cluster categories

Sira Gratz, Alexandra Zvonareva^*

^*Corresponding author af dette arbejde

Institut for Matematik

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review

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Abstract

We classify t-structures and thick subcategories in discrete cluster categories $\mathcal{C}(\mathcal{Z})$ of Dynkin type $A$, and show that the set of all t-structures on $\mathcal{C}(\mathcal{Z})$ is a lattice under inclusion of aisles, with meet given by their intersection. We show that both the lattice of t-structures on $\mathcal{C}(\mathcal{Z})$ obtained in this way and the lattice of thick subcategories of $\mathcal{C}(\mathcal{Z})$ are intimately related to the lattice of non-crossing partitions of type $A$. In particular, the lattice of equivalence classes of non-degenerate t-structures on such a category is isomorphic to the lattice of non-crossing partitions of a finite linearly ordered set.

Originalsprog	Engelsk
Tidsskrift	Journal of the London Mathematical Society,
Vol/bind	107
Nummer	3
Sider (fra-til)	973-1001
Antal sider	29
DOI	https://doi.org/10.1112/jlms.12705
Status	Udgivet - mar. 2023

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math.RT
math.CT
18E40, 06A12

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10.1112/jlms.12705Licens: CC BY

2110.08606v1

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title = "Lattices of t-structures and thick subcategories for discrete cluster categories",

abstract = " We classify t-structures and thick subcategories in discrete cluster categories $\mathcal{C}(\mathcal{Z})$ of Dynkin type $A$, and show that the set of all t-structures on $\mathcal{C}(\mathcal{Z})$ is a lattice under inclusion of aisles, with meet given by their intersection. We show that both the lattice of t-structures on $\mathcal{C}(\mathcal{Z})$ obtained in this way and the lattice of thick subcategories of $\mathcal{C}(\mathcal{Z})$ are intimately related to the lattice of non-crossing partitions of type $A$. In particular, the lattice of equivalence classes of non-degenerate t-structures on such a category is isomorphic to the lattice of non-crossing partitions of a finite linearly ordered set. ",

keywords = "math.RT, math.CT, 18E40, 06A12",

author = "Sira Gratz and Alexandra Zvonareva",

note = "Publisher Copyright: {\textcopyright} 2023 The Authors. Journal of the London Mathematical Society is copyright {\textcopyright} London Mathematical Society.",

year = "2023",

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T1 - Lattices of t-structures and thick subcategories for discrete cluster categories

AU - Gratz, Sira

AU - Zvonareva, Alexandra

PY - 2023/3

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N2 - We classify t-structures and thick subcategories in discrete cluster categories $\mathcal{C}(\mathcal{Z})$ of Dynkin type $A$, and show that the set of all t-structures on $\mathcal{C}(\mathcal{Z})$ is a lattice under inclusion of aisles, with meet given by their intersection. We show that both the lattice of t-structures on $\mathcal{C}(\mathcal{Z})$ obtained in this way and the lattice of thick subcategories of $\mathcal{C}(\mathcal{Z})$ are intimately related to the lattice of non-crossing partitions of type $A$. In particular, the lattice of equivalence classes of non-degenerate t-structures on such a category is isomorphic to the lattice of non-crossing partitions of a finite linearly ordered set.

AB - We classify t-structures and thick subcategories in discrete cluster categories $\mathcal{C}(\mathcal{Z})$ of Dynkin type $A$, and show that the set of all t-structures on $\mathcal{C}(\mathcal{Z})$ is a lattice under inclusion of aisles, with meet given by their intersection. We show that both the lattice of t-structures on $\mathcal{C}(\mathcal{Z})$ obtained in this way and the lattice of thick subcategories of $\mathcal{C}(\mathcal{Z})$ are intimately related to the lattice of non-crossing partitions of type $A$. In particular, the lattice of equivalence classes of non-degenerate t-structures on such a category is isomorphic to the lattice of non-crossing partitions of a finite linearly ordered set.

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KW - math.CT

KW - 18E40, 06A12

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DO - 10.1112/jlms.12705

M3 - Journal article

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SP - 973

EP - 1001

JO - Journal of the London Mathematical Society,

JF - Journal of the London Mathematical Society,

IS - 3

ER -

Lattices of t-structures and thick subcategories for discrete cluster categories

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