{
  "id": "2108.00260",
  "version": "v1",
  "published": "2021-07-31T15:09:25.000Z",
  "updated": "2021-07-31T15:09:25.000Z",
  "title": "Pseudo-symmetric pairs for Kac-Moody algebras",
  "authors": [
    "Vidas Regelskis",
    "Bart Vlaar"
  ],
  "comment": "42 pages, 7 tables",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "Involutive automorphisms of the second kind of Kac-Moody algebras and their fixed-point subalgebras can be q-deformed following Letzter and Kolb. These q-deformed algebras play a major role in the theory of the reflection equation. Essentially the same constructions can be made in a larger setting, where the automorphism is required to act involutively only on a stable Cartan subalgebra. We give a comprehensive Lie- and Coxeter-theoretic discussion of pseudo-involutions, pseudo-fixed-point subalgebras, including a survey of the associated restricted root systems and Weyl groups in the Kac-Moody setting, in terms of generalizations of Satake diagrams.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-31T15:09:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B22",
      "17B40",
      "17B67",
      "16B30",
      "17B37",
      "20F55"
    ],
    "keywords": [
      "kac-moody algebras",
      "pseudo-symmetric pairs",
      "q-deformed algebras play",
      "major role",
      "reflection equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}