{
  "annotation_id": "3e8d9bab-50b9-415d-a151-720717a31b7f",
  "date_created": "2026-03-02T18:01:28.066000Z",
  "date_modified": "2026-03-02T18:01:28.066000Z",
  "file_hash": "f896a86dfd0e27d61d1e9ebc341153cabfa905fcdc4541817c103b012df1a6da",
  "private": false,
  "record": {
    "abstract": "We introduce the notion of difference equation defined on a structured set.\nThe symmetry group of the structure determines the set of difference operators.\nAll main notions in the theory of difference equations are introduced as\ninvariants of the symmetry group. Linear equations are modules over the skew\ngroup algebra, solutions are morphisms relating a given equation to other\nequations,symmetries of an equation are module endomorphisms and conserved\nstructures are invariants in the tensor algebra of the given equation. We show\nthat the equations and their solutions can be described through representations\nof the isotropy group of the symmetry group of the underluing set. We relate\nour notion of difference equations and solutions to systems of classical\ndifference equations and their solutions and show that our notions include\nthese as a special case.",
    "arxiv_id": "q-alg/9712044",
    "authors": [
      "Per K. Jakobsen",
      "Valentin V. Lychagin"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "title": "Theory of linear G-difference equations",
    "url": "https://arxiv.org/abs/q-alg/9712044"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "5bdaa928-a088-4cff-ab3b-82fdc65dd8fe",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}