{
  "schema_version": 1,
  "kind": "ConceptView",
  "producer": "concept-view-1",
  "concept_id": "urn:uuid:91c6b7de-78fd-4b5a-9d1e-2b69ee97ba8e",
  "labels": {
    "zh-CN": "有限群",
    "en": "finite group"
  },
  "alternative_labels": [],
  "scope_note": "",
  "identity_status": "active",
  "identity_revision": "ea3326afaf18d6ff5b1d9ed74767ae66772ec18f0849ef77a2111b23845bf790",
  "occurrences": [
    {
      "concept_id": "urn:uuid:91c6b7de-78fd-4b5a-9d1e-2b69ee97ba8e",
      "book_id": "szekeres",
      "edition_id": "source-snapshot-bc3404156f6e",
      "lang": "zh-CN",
      "route": "zh/chapter-02/01-elements-of-group-theory",
      "anchor": "concept-2-finite-group",
      "chapter": "2",
      "section": "2.1",
      "offset": 5288,
      "range": [
        9819,
        10048
      ],
      "source_revision": "ad9d6c5a6bcd992ad92802c42b86c6bf56d20c316c26e232554fab59e18fbd9d",
      "source_category": "translation",
      "review_status": "unreviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "explicit-source-uuid-marker"
      },
      "label": "有限群(finite group)",
      "context": {
        "range": [
          9802,
          10284
        ],
        "quote": "由有限个元素组成的群 $G$ 称为<u id=\"concept-2-finite-group\" class=\"concept-term\" data-concept-identity=\"urn:uuid:91c6b7de-78fd-4b5a-9d1e-2b69ee97ba8e\" data-concept-route=\"/concept-identities#concept-91c6b7de-78fd-4b5a-9d1e-2b69ee97ba8e\">有限群(finite group)</u>。$G$中元素的个数称为其<u id=\"concept-2-order\" class=\"concept-term\" data-concept-identity=\"urn:uuid:38710033-3794-4234-8bbd-5f060b249b28\" data-concept-route=\"/concept-identities#concept-38710033-3794-4234-8bbd-5f060b249b28\">阶(order)</u>，用$|G|$表示。",
        "quote_sha256": "1572f00726e75df837ec2d7cd8174d01d01e85e9800202aab8d102a48ef6af4b",
        "environment": null,
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "en/chapter-02/01-elements-of-group-theory",
          "lang": "en",
          "source_category": "original_transcription",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-352d555605ce5e7de8c2df79"
    },
    {
      "concept_id": "urn:uuid:91c6b7de-78fd-4b5a-9d1e-2b69ee97ba8e",
      "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-bbdbf409a34a3551c1be-zh",
      "chapter": "1",
      "section": "1.3",
      "offset": 1672,
      "range": [
        13216,
        13512
      ],
      "source_revision": "4ee587fc4d72d2916ca8f6bce8080ecd42e2ae3d45d92d067027a95982f00008",
      "source_category": "translation",
      "review_status": "unreviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "explicit-source-uuid-marker"
      },
      "label": "有限群(finite group)",
      "context": {
        "range": [
          13200,
          14446
        ],
        "quote": "若群的元素只有有限多个，就称为[<u class=\"concept-term\" data-concept-reference=\"concepts/group-theory/finite-group\" data-concept-identity=\"urn:uuid:91c6b7de-78fd-4b5a-9d1e-2b69ee97ba8e\" data-concept-route=\"/concept-identities#concept-91c6b7de-78fd-4b5a-9d1e-2b69ee97ba8e\" id=\"first-bbdbf409a34a3551c1be-zh\">有限群(finite group)</u>](../../../../../concepts/group-theory/finite-group)。有限群理论及其在量子力学中的应用已相当成熟，但本书大多略过这一主题，转而研究元素个数无限的[<u class=\"concept-term\" data-concept-reference=\"concepts/group-theory/lie-group\" data-concept-identity=\"urn:uuid:8c364498-0e05-4c91-8fd7-1730d6e8656e\" data-concept-route=\"/concept-identities#concept-8c364498-0e05-4c91-8fd7-1730d6e8656e\">李群(Lie group)</u>](../../../../../concepts/group-theory/lie-group)。李群的元素构成某个维数的几何空间；选取局部坐标后，群运算由可微函数给出。本书讨论的大多数李群都是<span id=\"concept-1-matrix-group\" class=\"block-anchor\"></span><u class=\"concept-term\" data-concept-id=\"concept-1-matrix-group\" data-concept-role=\"discussion\" data-concept-identity=\"urn:uuid:05f42bf3-d38b-49e0-bed7-1d0452d9ac3d\" data-concept-route=\"/concept-identities#concept-05f42bf3-d38b-49e0-bed7-1d0452d9ac3d\" id=\"first-fc558e266a7590e7bf39-zh\">矩阵群(matrix group)</u>，也就是由 $n\\times n$ 可逆实矩阵或复矩阵构成的矩阵群的子群。此时群乘法就是矩阵乘法。一个将详细讨论的例子是三维空间中绕某一点旋转所构成的群；这些旋转可以表示为 $3\\times3$ 矩阵，旋转的复合对应矩阵乘法。",
        "quote_sha256": "893b57706d2fdfe1cf5b4abe748894ccea377ac4f088dc3439127ea5620d86d4",
        "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-67dcbc38e4933fee0a20800d"
    }
  ],
  "registered_positions": [
    {
      "route": "zh/chapter-02/01-elements-of-group-theory",
      "lang": "zh-CN",
      "section": "2.1",
      "signal": "term-mark",
      "label": "有限群",
      "english": "finite group",
      "offset": 3572
    },
    {
      "route": "books/woit-qtgr/2025-10-20/zh/chapter-01/03-unitary-group-representations",
      "lang": "zh-CN",
      "section": "1.3",
      "signal": "term-mark",
      "label": "有限群",
      "english": "finite group",
      "offset": 1235
    }
  ],
  "statements": [],
  "resolved_references": [],
  "reading_order": [
    "occ-352d555605ce5e7de8c2df79",
    "occ-67dcbc38e4933fee0a20800d"
  ],
  "recorded_dependencies": [],
  "reading_paths": [],
  "coverage": {
    "registered_positions": 2,
    "located_occurrences": 2,
    "whole_book_search_complete": false,
    "registered_positions_truncated": false,
    "independent_human_review_implied": false
  },
  "unresolved": [],
  "base_revision": "6891c6c726b800b1e0ec9e394d78b108fdd2754aac989509e1193c42283c8ba6",
  "optional_enrichments": []
}
