{
  "id": "2301.09847",
  "version": "v1",
  "published": "2023-01-24T07:11:54.000Z",
  "updated": "2023-01-24T07:11:54.000Z",
  "title": "Non-degeneracy results for (multi-)pushouts of compact groups",
  "authors": [
    "Alexandru Chirvasitu"
  ],
  "comment": "24 pages + references",
  "categories": [
    "math.GR",
    "math.CT",
    "math.GN",
    "math.RT"
  ],
  "abstract": "We prove that embeddings of compact groups are equalizers, and a number of results on pushouts (and more generally, amalgamated free products) in the category of compact groups. Call a family of compact-group embeddings $H\\le G_i$ {\\it algebraically sound} if the corresponding group-theoretic pushout embeds in its Bohr compactification. We (a) show that a family of normal embeddings is algebraically sound in the sense that $G_i$ admit embeddings $G_i\\le G$ into a compact group which agree on $H$; (b) give equivalent characterizations of coherently embeddable families of normal embeddings in representation-theoretic terms, via Clifford theory; (c) characterize those compact connected Lie groups $H$ for which all finite families of normal embeddings $H\\trianglelefteq G_i$ are coherently embeddable as those whose centers do not contain 2-tori, and (d) show that families of {\\it split} embeddings of compact groups are always algebraically sound.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-24T07:11:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22C05",
      "18A30",
      "22A05",
      "18A20",
      "22E46",
      "22D10",
      "54A10"
    ],
    "keywords": [
      "compact group",
      "non-degeneracy results",
      "normal embeddings",
      "algebraically sound",
      "corresponding group-theoretic pushout embeds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}