TY - JOUR
T1 - Cotorsion torsion triples and the representation theory of filtered hierarchical clustering
AU - Bauer, Ulrich
AU - Botnan, Magnus B.
AU - Oppermann, Steffen
AU - Steen, Johan
PY - 2020/8/5
Y1 - 2020/8/5
N2 - 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.
AB - 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.
KW - Hierarchical clustering
KW - Multiparameter persistence
KW - Quiver representation theory
KW - Torsion theory
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U2 - 10.1016/j.aim.2020.107171
DO - 10.1016/j.aim.2020.107171
M3 - Article
AN - SCOPUS:85083809353
VL - 369
SP - 1
EP - 51
JO - Advances in Mathematics
JF - Advances in Mathematics
SN - 0001-8708
M1 - 107171
ER -