{
  "schema_version": 1,
  "kind": "ConceptView",
  "producer": "concept-view-1",
  "concept_id": "urn:uuid:517f0a9d-f274-4f99-8731-9dc921f8c7ac",
  "labels": {
    "zh-CN": "李群同态",
    "en": "Lie group homomorphism"
  },
  "alternative_labels": [],
  "scope_note": "",
  "identity_status": "active",
  "identity_revision": "d0a6afd9491549cf466cdd984c1d3ad30584d5f1ea466dd8b9aaa5a78a983a5a",
  "occurrences": [
    {
      "concept_id": "urn:uuid:517f0a9d-f274-4f99-8731-9dc921f8c7ac",
      "book_id": "szekeres",
      "edition_id": "source-snapshot-bc3404156f6e",
      "lang": "en",
      "route": "en/chapter-19/02-the-exponential-map",
      "anchor": "first-8d142d52dd94eda1ef5f-en",
      "chapter": "19",
      "section": "19.2",
      "offset": 333,
      "range": [
        4171,
        4412
      ],
      "source_revision": "2023cc129281e7cec539833fb2be307624bd5cdb8487aedcd515bd18662316a8",
      "source_category": "original_transcription",
      "review_status": "unreviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "explicit-source-uuid-marker"
      },
      "label": "Lie group homomorphism",
      "context": {
        "range": [
          4169,
          4902
        ],
        "quote": "A <u class=\"concept-term\" data-concept-identity=\"urn:uuid:517f0a9d-f274-4f99-8731-9dc921f8c7ac\" data-concept-route=\"/concept-identities#concept-517f0a9d-f274-4f99-8731-9dc921f8c7ac\" id=\"first-8d142d52dd94eda1ef5f-en\">Lie group homomorphism</u> between two Lie groups $G$ and $H$ is a differentiable map $\\varphi : G \\to H$ that is a group homomorphism, $\\varphi ( g h ) = \\varphi ( g ) \\varphi ( h )$ for all $g , h \\in G$ . In the case where it is a diffeomorphism $\\varphi$ is said to be a <u class=\"concept-term\" data-concept-identity=\"urn:uuid:537f5597-841d-4de6-85fe-976eb10c7db7\" data-concept-route=\"/concept-identities#concept-537f5597-841d-4de6-85fe-976eb10c7db7\" id=\"first-ff53abc2bdcb7a599733-en\">Lie group isomorphism</u>.",
        "quote_sha256": "8b772f8dca5c08226260f51c6bfc43d0a0cbbb68c1630b45948cca35db74f2f9",
        "environment": null,
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "zh/chapter-19/02-the-exponential-map",
          "lang": "zh-CN",
          "source_category": "translation",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-5ea9a8c4e5b4f89bed15317c"
    },
    {
      "concept_id": "urn:uuid:517f0a9d-f274-4f99-8731-9dc921f8c7ac",
      "book_id": "szekeres",
      "edition_id": "source-snapshot-bc3404156f6e",
      "lang": "zh-CN",
      "route": "zh/chapter-19/02-the-exponential-map",
      "anchor": "concept-19-lie-group-homomorphism",
      "chapter": "19",
      "section": "19.2",
      "offset": 350,
      "range": [
        4695,
        4946
      ],
      "source_revision": "976e51ba6ea8791a151bec83268d16111acbb39b1972c87cf741c6875c2e61c6",
      "source_category": "translation",
      "review_status": "unreviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "explicit-source-uuid-marker"
      },
      "label": "李群同态(Lie group homomorphism)",
      "context": {
        "range": [
          4676,
          5325
        ],
        "quote": "两个李群 $G$ 与 $H$ 之间的 <u id=\"concept-19-lie-group-homomorphism\" class=\"concept-term\" data-concept-identity=\"urn:uuid:517f0a9d-f274-4f99-8731-9dc921f8c7ac\" data-concept-route=\"/concept-identities#concept-517f0a9d-f274-4f99-8731-9dc921f8c7ac\">李群同态(Lie group homomorphism)</u> 是一个可微映射 $\\varphi : G \\to H$，并且是群同态，即对所有 $g , h \\in G$ 都有 $\\varphi ( g h ) = \\varphi ( g ) \\varphi ( h )$。若它是微分同胚，则称 $\\varphi$ 为 <u id=\"concept-19-lie-group-isomorphism\" class=\"concept-term\" data-concept-identity=\"urn:uuid:537f5597-841d-4de6-85fe-976eb10c7db7\" data-concept-route=\"/concept-identities#concept-537f5597-841d-4de6-85fe-976eb10c7db7\">李群同构(Lie group isomorphism)</u>。",
        "quote_sha256": "14fe97712a3bc207d1166754d4f84dd814a53d01c9832917df5d1a1bf46849d1",
        "environment": null,
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "en/chapter-19/02-the-exponential-map",
          "lang": "en",
          "source_category": "original_transcription",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-d6b7490be7922c586f0bab7b"
    }
  ],
  "registered_positions": [
    {
      "route": "en/chapter-19/02-the-exponential-map",
      "lang": "en",
      "section": "19.2",
      "signal": "term-mark",
      "label": "Lie group homomorphism",
      "english": "Lie group homomorphism",
      "offset": 333
    },
    {
      "route": "zh/chapter-19/02-the-exponential-map",
      "lang": "zh-CN",
      "section": "19.2",
      "signal": "term-mark",
      "label": "李群同态",
      "english": "Lie group homomorphism",
      "offset": 350
    }
  ],
  "statements": [],
  "resolved_references": [],
  "reading_order": [
    "occ-5ea9a8c4e5b4f89bed15317c",
    "occ-d6b7490be7922c586f0bab7b"
  ],
  "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": "4e19a630f185d47be82557ef43d958b27eb3d389a8703aa87527918a4cecafa8",
  "optional_enrichments": []
}