{
  "id": "2107.01530",
  "version": "v1",
  "published": "2021-07-04T03:28:24.000Z",
  "updated": "2021-07-04T03:28:24.000Z",
  "title": "On Reflection Representations of Coxeter Groups over Non-Commutative Rings",
  "authors": [
    "Annette Pilkingtonn"
  ],
  "comment": "28 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "In this paper, we consider representations of Coxeter groups over a path algebra, R, defined by Dyer. We answer a question posed by Dyer about the multiplicative properties of R, showing that it is \"almost a domain\". We also show that R cam be embedded in a matrix ring over a free product of extension fields of the rational numbers and rings of Laurent polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-04T03:28:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F55",
      "20C99"
    ],
    "keywords": [
      "coxeter groups",
      "reflection representations",
      "non-commutative rings",
      "laurent polynomials",
      "free product"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}