Cotorsion torsion triples and the representation theory of filtered hierarchical clustering

Ulrich Bauer, Magnus B. Botnan, Steffen Oppermann, Johan Steen

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

We give a full classification of representation types of the subcategories of representations of an m×n rectangular grid with monomorphisms (dually, epimorphisms) in one or both directions, which appear naturally in the context of clustering as two-parameter persistent homology in degree zero. We show that these subcategories are equivalent to the category of all representations of a smaller grid, modulo a finite number of indecomposables. This equivalence is constructed from a certain cotorsion torsion triple, which is obtained from a tilting subcategory generated by said indecomposables.

Original languageEnglish
Article number107171
JournalAdvances in Mathematics
Volume369
DOIs
StatePublished - 5 Aug 2020

Keywords

  • Hierarchical clustering
  • Multiparameter persistence
  • Quiver representation theory
  • Torsion theory

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