{
  "schema_version": 1,
  "kind": "ConceptView",
  "producer": "concept-view-1",
  "concept_id": "urn:uuid:1c8384ff-2641-4168-ba63-d81a2dffcea1",
  "labels": {
    "zh-CN": "表示的次数",
    "en": "degree of a representation"
  },
  "alternative_labels": [],
  "scope_note": "",
  "identity_status": "active",
  "identity_revision": "407c5f7906fd810aed98f098e5c8a22535c3c2f473f72ae6ae92c36b68443408",
  "occurrences": [
    {
      "concept_id": "urn:uuid:1c8384ff-2641-4168-ba63-d81a2dffcea1",
      "book_id": "szekeres",
      "edition_id": "source-snapshot-bc3404156f6e",
      "lang": "zh-CN",
      "route": "zh/chapter-04/04-introduction-to-group-representation-theory",
      "anchor": "concept-4-degree-of-a-representation",
      "chapter": "4",
      "section": "4.4",
      "offset": 1292,
      "range": [
        6390,
        6649
      ],
      "source_revision": "8659a22bf0394df6e0f0547cc91ed5a8dd18c3b22a3aa2463bbac9fbfc4f313c",
      "source_category": "translation",
      "review_status": "unreviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "explicit-source-uuid-marker"
      },
      "label": "表示的次数(degree of a representation)",
      "context": {
        "range": [
          5985,
          6690
        ],
        "quote": "本质上，抽象群的表示是将群的元素具体模型化为向量空间上的线性变换的一种方式。若该表示是一一对应的，即若 $\\ker$ $T = \\{ e \\}$ ，则称该表示为 <u id=\"concept-4-faithful-representation\" class=\"concept-term\" data-concept-identity=\"urn:uuid:c1e17053-8805-4fd9-93e0-eb9997fdaf8f\" data-concept-route=\"/concept-identities#concept-c1e17053-8805-4fd9-93e0-eb9997fdaf8f\">忠实表示(faithful representation)</u> 。尽管原则上 $V$ 既可以是实向量空间也可以是复向量空间，我们将主要考虑复向量空间上的表示。若 $V$ 是有限维的，则其维数 $n$ 称为 <u id=\"concept-4-degree-of-a-representation\" class=\"concept-term\" data-concept-identity=\"urn:uuid:1c8384ff-2641-4168-ba63-d81a2dffcea1\" data-concept-route=\"/concept-identities#concept-1c8384ff-2641-4168-ba63-d81a2dffcea1\">表示的次数(degree of a representation)</u> 。我们将几乎完全限于关注有限次数的表示。群表示论在[6–8]中有更为详细的展开。",
        "quote_sha256": "71f7fae0da54813f1f535dba21e51fbfff534afdcd0670f76b73055490e32c2c",
        "environment": null,
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "en/chapter-04/04-introduction-to-group-representation-theory",
          "lang": "en",
          "source_category": "original_transcription",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-3e59c4c0e54d16e0b955fc65"
    }
  ],
  "registered_positions": [
    {
      "route": "zh/chapter-04/04-introduction-to-group-representation-theory",
      "lang": "zh-CN",
      "section": "4.4",
      "signal": "term-mark",
      "label": "表示的次数",
      "english": "degree of a representation",
      "offset": 980
    }
  ],
  "statements": [],
  "resolved_references": [],
  "reading_order": [
    "occ-3e59c4c0e54d16e0b955fc65"
  ],
  "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": "e6eaf0690d05c3827a996e3e1f0c0387c12da2ddd8c225f7dbcfd91bd7bbdd90",
  "optional_enrichments": []
}