{
  "annotation_id": "233c31c4-8b8a-4e71-b3e1-0e0b62247c9a",
  "date_created": "2026-02-17T05:53:08.558000Z",
  "date_modified": "2026-02-17T05:53:08.558000Z",
  "file_hash": "af4ed841a1267359a9fd05cdc5b3bf21dcbbde2171805ee17886f3ad2cd4d9f1",
  "private": false,
  "record": {
    "abstract": "We classify all $G$-invariant von Neumann subalgebras in $L(G)$ for $G=\\mathbb{Z}^2\\rtimes SL_2(\\mathbb{Z})$. This is the first result on classifying $G$-invariant von Neumann subalgebras in $L(G)$ for i.c.c. groups $G$ without the invariant von Neumann subalgebras rigidity property (ISR property for short) as introduced in Amrutam-Jiang\u0027s work. As a corollary, we show that $L(\\mathbb{Z}^2\\rtimes \\{\\pm I_2\\})$ is the unique maximal Haagerup $G$-invariant von Neumann subalgebra in $L(G)$, where $I_2$ denotes the identity matrix in $SL_2(\\mathbb{Z})$.",
    "arxiv_id": "2601.06350",
    "authors": [
      "Yongle Jiang",
      "Ruoyu Liu"
    ],
    "categories": [
      "math.OA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "On invariant subalgebras when the ISR property fails",
    "url": "https://arxiv.org/abs/2601.06350",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "88f9fd16-7802-496a-9a17-790da2b79bbf",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}