{
  "id": "2407.07028",
  "version": "v1",
  "published": "2024-07-09T16:47:51.000Z",
  "updated": "2024-07-09T16:47:51.000Z",
  "title": "On semi-simplicity of KMY algebras",
  "authors": [
    "Nouf Alraddadi",
    "Alison Parker"
  ],
  "comment": "21 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We study the algebras, $J_{l,n}(\\delta)$, introduced by Kadar-Martin-Yu in arXiv:1401.1774. We show that these algebras are iterated inflation algebras. We give a set of generators for $J_{l,n}(\\delta)$. We show that this algebra satisifies the CMPX axiomatic framework in arXiv:math/0411395 when the base field is the complex numbers and $\\delta \\ne 0$. We show that $J_{l,n}(\\delta)$ is semisimple over the complex numbers if $\\delta$ is complex and not real.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-09T16:47:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G99",
      "20G05",
      "20G10"
    ],
    "keywords": [
      "kmy algebras",
      "semi-simplicity",
      "complex numbers",
      "cmpx axiomatic framework",
      "base field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}