{
  "id": "2408.13527",
  "version": "v1",
  "published": "2024-08-24T09:00:49.000Z",
  "updated": "2024-08-24T09:00:49.000Z",
  "title": "The inter-relationship between isomorphisms of commutative and isomorphisms of non-commutative $\\log$-algebras",
  "authors": [
    "Rustam Abdullaev",
    "Azizkhon Azizov"
  ],
  "comment": "8 pages",
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "This paper establishes a necessary and sufficient condition for the coincidence of non-commutative $\\log$-algebras constructed from different exact normal semifinite traces. Consequently, we provide a criterion for the isomorphism of $\\log$-algebras built on non-commutative von Neumann algebras with different exact normal semifinite traces. Additionally, we demonstrate a connection between the isomorphism of non-commutative $\\log$-algebras and the isomorphism of the corresponding $\\log$-algebras constructed on the center of these von Neumann algebras. Furthermore, we present a necessary and sufficient condition for the isomorphism of $\\log$-algebras derived from different von Neumann algebras of type $I_n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-24T09:00:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46A16",
      "46B04",
      "46E30"
    ],
    "keywords": [
      "isomorphism",
      "exact normal semifinite traces",
      "inter-relationship",
      "sufficient condition",
      "non-commutative von neumann algebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}