{
  "id": "1811.08946",
  "version": "v1",
  "published": "2018-11-21T20:54:39.000Z",
  "updated": "2018-11-21T20:54:39.000Z",
  "title": "Decomposition of persistence modules",
  "authors": [
    "Magnus Bakke Botnan",
    "William Crawley-Boevey"
  ],
  "comment": "16 pages",
  "categories": [
    "math.RT",
    "math.AT"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-21T20:54:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "decomposition",
      "pointwise finite-dimensional persistence module",
      "small category decomposes",
      "local endomorphism rings",
      "fundamental structure theorems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}