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...
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Published in | Algebras and representation theory Vol. 26; no. 6; pp. 3003 - 3046 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Dordrecht
Springer Netherlands
01.12.2023
Springer Nature B.V Springer Verlag |
Subjects | |
Online Access | Get full text |
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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. |
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ISSN: | 1386-923X 1572-9079 |
DOI: | 10.1007/s10468-022-10189-4 |