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

2021/10/16 by Sira Gratz, Gratz, Sira, Alexandra Zvonareva +1 · 2 citations
Mathematics · #06A12 #18E40 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2110.08606

openalex publication_date 2021/10/16 · openalex created_date 2023/01/06 · openalex updated_date 2026/07/28

Abstract

We classify t-structures and thick subcategories in discrete cluster categories C(Z) of Dynkin type A, and show that the set of all t-structures on C(Z) is a lattice under inclusion of aisles, with meet given by their intersection. We show that both the lattice of t-structures on C(Z) obtained in this way and the lattice of thick subcategories of C(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.

Cited by

• Triangulated Categories Admitting Linear Generators
• Negative Calabi-Yau discrete cluster categories via Nakayama representations and persistence theory

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