Local Characterizations for Decomposability of 2-Parameter Persistence Modules

We investigate the existence of sufficient local conditions under which poset representations decompose as direct sums of indecomposables from a given class. In our work, the indexing poset is the product of two totally ordered sets, corresponding to the setting of 2-parameter persistence in topolog...

Full description

Saved in:
Bibliographic Details
Published inAlgebras and representation theory Vol. 26; no. 6; pp. 3003 - 3046
Main Authors Botnan, Magnus B., Lebovici, Vadim, Oudot, Steve
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.12.2023
Springer Nature B.V
Springer Verlag
Subjects
Associative Rings and Algebras
Commutative Rings and Algebras
Data analysis
Decomposition
Mathematics
Mathematics and Statistics
Modules
Non-associative Rings and Algebras
Parameters
Representation Theory
Representations
Set theory
55N31
Representation theory
16G20
Topological data analysis
Multiparameter persistence
Online AccessGet full text

Cover

More Information
Summary:We investigate the existence of sufficient local conditions under which poset representations decompose as direct sums of indecomposables from a given class. In our work, the indexing poset is the product of two totally ordered sets, corresponding to the setting of 2-parameter persistence in topological data analysis. Our indecomposables of interest belong to the so-called interval modules, which by definition are indicator representations of intervals in the poset. While the whole class of interval modules does not admit such a local characterization, we show that the subclass of rectangle modules does admit one and that it is, in some precise sense, the largest subclass to do so.
ISSN:1386-923X
1572-9079
DOI:10.1007/s10468-022-10189-4