{
  "id": "2204.07093",
  "version": "v1",
  "published": "2022-04-14T16:33:37.000Z",
  "updated": "2022-04-14T16:33:37.000Z",
  "title": "A Halmos-von Neumann theorem for actions of general groups",
  "authors": [
    "Patrick Hermle",
    "Henrik Kreidler"
  ],
  "categories": [
    "math.DS",
    "math.RT"
  ],
  "abstract": "We give a new categorical approach to the Halmos-von Neumann theorem for actions of general topological groups. As a first step, we establish that the categories of topological and measure-preserving irreducible systems with discrete spectrum are equivalent. This allows to prove the Halmos-von Neumann theorem in the framework of topological dynamics. We then use the Pontryagin and Tannaka-Krein duality theories to obtain classification results for topological and then measure-preserving systems with discrete spectrum. As a byproduct, we obtain a complete isomorphism invariant for compactifications of a fixed topological group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-14T16:33:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A15",
      "37B05",
      "43A40",
      "22C05"
    ],
    "keywords": [
      "halmos-von neumann theorem",
      "general groups",
      "discrete spectrum",
      "complete isomorphism invariant",
      "tannaka-krein duality theories"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}