Decomposition of persistence modules

Magnus Bakke Botnan; William Crawley-Boevey

Decomposition of persistence modules

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arxiv 1811.08946 v3 pith:GOIV3M23 submitted 2018-11-21 math.RT math.AT

Magnus Bakke Botnan , William Crawley-Boevey This is my paper · ORCID

classification math.RTmath.AT

keywords persistencemodulesapplicationcategorydecomposesdecompositiondirectendomorphism

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We show that a pointwise finite-dimensional persistence module indexed over a small category decomposes into a direct sum of indecomposables with local endomorphism rings. As an application of this result we give new, short proofs of fundamental structure theorems for persistence modules.

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Modules over posets: commutative and homological algebra
math.AC 2019-08 conditional novelty 8.0 of 10

Tame modules over arbitrary posets are proved to have finite encodings, fringe presentations, indicator resolutions, and primary decompositions, leading to proofs of two sheaf-theoretic conjectures.

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