{
  "schema_version": 1,
  "kind": "ConceptView",
  "producer": "concept-view-1",
  "concept_id": "urn:uuid:def3eb05-8eb2-451d-b5fb-2d8076b1e56a",
  "labels": {
    "zh-CN": "非交换群",
    "en": "non-commutative group"
  },
  "alternative_labels": [],
  "scope_note": "",
  "identity_status": "active",
  "identity_revision": "066c3151c923859c1cf08d2b9c422dba58ae224c92654eaf37d0ef88a5c9efea",
  "occurrences": [
    {
      "concept_id": "urn:uuid:def3eb05-8eb2-451d-b5fb-2d8076b1e56a",
      "book_id": "woit-qtgr",
      "edition_id": "2025-10-20",
      "lang": "zh-CN",
      "route": "books/woit-qtgr/2025-10-20/zh/chapter-01/03-unitary-group-representations",
      "anchor": "first-48371028521ae40800e1-zh",
      "chapter": "1",
      "section": "1.3",
      "offset": 8312,
      "range": [
        19856,
        20183
      ],
      "source_revision": "4ee587fc4d72d2916ca8f6bce8080ecd42e2ae3d45d92d067027a95982f00008",
      "source_category": "translation",
      "review_status": "unreviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "explicit-source-uuid-marker"
      },
      "label": "非交换群(non-commutative group)",
      "context": {
        "range": [
          19305,
          20222
        ],
        "quote": "- 群 $G_2=O(3)$，即[<u class=\"concept-term\" data-concept-reference=\"concepts/linear-algebra/orthogonal-group\" data-concept-identity=\"urn:uuid:9c0cba6a-c2b4-4c44-b15e-b04e84d239af\" data-concept-route=\"/concept-identities#concept-9c0cba6a-c2b4-4c44-b15e-b04e84d239af\" id=\"first-bbb06fbb334ea918614f-zh\">正交群(orthogonal group)</u>](../../../../../concepts/linear-algebra/orthogonal-group)，由 $\\mathbf R^3$ 的三维正交变换组成，并作用于 $\\mathbf R^3$。这些变换是绕原点的旋转，也可能是旋转与一次反射的复合。注意，此处运算次序很重要：对于 $O(3)$ 这样的<span id=\"concept-1-non-commutative-group\" class=\"block-anchor\"></span><u class=\"concept-term\" data-concept-id=\"concept-1-non-commutative-group\" data-concept-role=\"discussion\" data-concept-identity=\"urn:uuid:def3eb05-8eb2-451d-b5fb-2d8076b1e56a\" data-concept-route=\"/concept-identities#concept-def3eb05-8eb2-451d-b5fb-2d8076b1e56a\" id=\"first-48371028521ae40800e1-zh\">非交换群(non-commutative group)</u>，某些群元素 $g_1,g_2$ 满足 $g_1g_2\\ne g_2g_1$。",
        "quote_sha256": "8bb83541331032d6927a32579c2ec834c05c58950adb9473aef9fecac143fd94",
        "environment": null,
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "books/woit-qtgr/2025-10-20/en/chapter-01/03-unitary-group-representations",
          "lang": "en",
          "source_category": "original_transcription",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-69770b52b2972d5640dad6a2"
    }
  ],
  "registered_positions": [
    {
      "route": "books/woit-qtgr/2025-10-20/zh/chapter-01/03-unitary-group-representations",
      "lang": "zh-CN",
      "section": "1.3",
      "signal": "term-mark",
      "label": "非交换群",
      "english": "non-commutative group",
      "offset": 5141
    }
  ],
  "statements": [],
  "resolved_references": [],
  "reading_order": [
    "occ-69770b52b2972d5640dad6a2"
  ],
  "recorded_dependencies": [],
  "reading_paths": [],
  "coverage": {
    "registered_positions": 1,
    "located_occurrences": 1,
    "whole_book_search_complete": false,
    "registered_positions_truncated": false,
    "independent_human_review_implied": false
  },
  "unresolved": [],
  "base_revision": "f39ff545104eef1ef8899c4a08cba45a9d22ae4957fa6b5f23bd4a4723c8a78a",
  "optional_enrichments": []
}