Classifying t-structures via ICE-closed subcategories and a lattice of torsion classes

2023/07/21 by Arashi Sakai, Sakai, Arashi · 1 citation
Mathematics · Medicine · #16G10 #18E10 #18G80 #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Intracranial Aneurysms: Treatment and Complications #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2307.11347

openalex publication_date 2023/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In a triangulated category equipped with a t-structure, we investigate a relation between ICE-closed (=Image-Cokernel-Extension-closed) subcategories of the heart of the t-structure and aisles in the triangulated categories. We introduce an ICE sequence, a sequence of ICE-closed subcategories satisfying a certain condition, and establish a bijection between ICE sequences and homology-determined preaisles. Moreover we give a sufficient condition that an ICE sequence induces a t-structure via the bijection. In the case of the bounded derived category D^b(modΛ) of a τ-tilting finite algebra Λ, we give a description of ICE sequences in modΛ which induce bounded t-structures on D^b(modΛ) from the viewpoint of a lattice consisting of torsion classes in modΛ.

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