{
  "schema_version": 1,
  "kind": "ConceptView",
  "producer": "concept-view-1",
  "concept_id": "urn:uuid:c45f5876-ea6e-409e-b221-625213a50b9f",
  "labels": {
    "zh-CN": "李超代数表示",
    "en": "Representation of a Lie superalgebra"
  },
  "alternative_labels": [
    {
      "lang": "en",
      "value": "representation of a Lie superalgebra"
    }
  ],
  "scope_note": "",
  "identity_status": "active",
  "identity_revision": "d19769e4261a4da4013873377a859d1e825ac782a0fbf3346484c7b22d0903f0",
  "occurrences": [
    {
      "concept_id": "urn:uuid:c45f5876-ea6e-409e-b221-625213a50b9f",
      "book_id": "woit-qtgr",
      "edition_id": "2025-10-20",
      "lang": "zh-CN",
      "route": "books/woit-qtgr/2025-10-20/zh/chapter-31/01-quantization-of-pseudo-classical-systems",
      "anchor": "first-9fdbeb8fa684a62e53aa-zh",
      "chapter": "31",
      "section": "31.1",
      "offset": 524,
      "range": [
        8380,
        9036
      ],
      "source_revision": "90bac7a9d80e6e5cb33a6290a0d90908321c84b22117df85bc505aac74ac3af0",
      "source_category": "machine_draft",
      "review_status": "machine-draft-not-reviewed",
      "role": "definition",
      "role_basis": {
        "kind": "registered-source-environment",
        "registered_position": {
          "route": "books/woit-qtgr/2025-10-20/zh/chapter-31/01-quantization-of-pseudo-classical-systems",
          "lang": "zh-CN",
          "section": "31.1",
          "signal": "named-definition",
          "label": "李超代数表示",
          "english": "",
          "offset": 454
        }
      },
      "label": "> [!definition] 定义 · 李超代数表示",
      "context": {
        "range": [
          8380,
          9036
        ],
        "quote": "\n\n> [!definition] 定义 · 李超代数表示\n>\n> [<u class=\"concept-term\" data-concept-reference=\"concepts/representation-theory/lie-superalgebra-representation\" data-concept-identity=\"urn:uuid:c45f5876-ea6e-409e-b221-625213a50b9f\" data-concept-route=\"/concept-identities#concept-c45f5876-ea6e-409e-b221-625213a50b9f\" id=\"first-b64fd7ba5ab4854767e5-zh\">李超代数表示(representation of a Lie superalgebra)</u>](../../../../../concepts/representation-theory/lie-superalgebra-representation)是保持超括号的同态 $\\Phi$：\n>\n> $$\n> [\\Phi(X),\\Phi(Y)]_\\pm=\\Phi([X,Y]_\\pm).\n> $$\n>\n> 它取值于线性算符的李超代数，满足 $|\\Phi(X)|=|X|$，其中\n>\n> $$\n> [\\Phi(X),\\Phi(Y)]_\\pm=\\Phi(X)\\Phi(Y)-(-)^{|X||Y|}\\Phi(Y)\\Phi(X).\n> $$\n",
        "quote_sha256": "101cff568c7578d88e049dfe6f1b51b6fed99e9e739a136f49f5a5ae356ffa57",
        "environment": "definition",
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "books/woit-qtgr/2025-10-20/en/chapter-31/01-quantization-of-pseudo-classical-systems",
          "lang": "en",
          "source_category": "machine_draft",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-06b026e350335315e330d4c3"
    },
    {
      "concept_id": "urn:uuid:c45f5876-ea6e-409e-b221-625213a50b9f",
      "book_id": "woit-qtgr",
      "edition_id": "2025-10-20",
      "lang": "zh-CN",
      "route": "books/woit-qtgr/2025-10-20/zh/chapter-31/01-quantization-of-pseudo-classical-systems",
      "anchor": "first-b64fd7ba5ab4854767e5-zh",
      "chapter": "31",
      "section": "31.1",
      "offset": 559,
      "range": [
        8415,
        8766
      ],
      "source_revision": "90bac7a9d80e6e5cb33a6290a0d90908321c84b22117df85bc505aac74ac3af0",
      "source_category": "machine_draft",
      "review_status": "machine-draft-not-reviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "explicit-source-uuid-marker"
      },
      "label": "李超代数表示(representation of a Lie superalgebra)",
      "context": {
        "range": [
          8380,
          9036
        ],
        "quote": "\n\n> [!definition] 定义 · 李超代数表示\n>\n> [<u class=\"concept-term\" data-concept-reference=\"concepts/representation-theory/lie-superalgebra-representation\" data-concept-identity=\"urn:uuid:c45f5876-ea6e-409e-b221-625213a50b9f\" data-concept-route=\"/concept-identities#concept-c45f5876-ea6e-409e-b221-625213a50b9f\" id=\"first-b64fd7ba5ab4854767e5-zh\">李超代数表示(representation of a Lie superalgebra)</u>](../../../../../concepts/representation-theory/lie-superalgebra-representation)是保持超括号的同态 $\\Phi$：\n>\n> $$\n> [\\Phi(X),\\Phi(Y)]_\\pm=\\Phi([X,Y]_\\pm).\n> $$\n>\n> 它取值于线性算符的李超代数，满足 $|\\Phi(X)|=|X|$，其中\n>\n> $$\n> [\\Phi(X),\\Phi(Y)]_\\pm=\\Phi(X)\\Phi(Y)-(-)^{|X||Y|}\\Phi(Y)\\Phi(X).\n> $$\n",
        "quote_sha256": "101cff568c7578d88e049dfe6f1b51b6fed99e9e739a136f49f5a5ae356ffa57",
        "environment": "definition",
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "books/woit-qtgr/2025-10-20/en/chapter-31/01-quantization-of-pseudo-classical-systems",
          "lang": "en",
          "source_category": "machine_draft",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-b4888e470be538fb843d5a71"
    },
    {
      "concept_id": "urn:uuid:c45f5876-ea6e-409e-b221-625213a50b9f",
      "book_id": "woit-qtgr",
      "edition_id": "2025-10-20",
      "lang": "en",
      "route": "books/woit-qtgr/2025-10-20/en/chapter-31/01-quantization-of-pseudo-classical-systems",
      "anchor": "first-b64fd7ba5ab4854767e5-en",
      "chapter": "31",
      "section": "31.1",
      "offset": 951,
      "range": [
        7966,
        8704
      ],
      "source_revision": "323639751e7a7355386f87b2eada21802660b14be73d21d4f7d2491940c6fe64",
      "source_category": "machine_draft",
      "review_status": "machine-draft-not-reviewed",
      "role": "definition",
      "role_basis": {
        "kind": "registered-source-environment",
        "registered_position": {
          "route": "books/woit-qtgr/2025-10-20/en/chapter-31/01-quantization-of-pseudo-classical-systems",
          "lang": "en",
          "section": "31.1",
          "signal": "named-definition",
          "label": "Representation of a Lie superalgebra",
          "english": "Representation of a Lie superalgebra",
          "offset": 881
        }
      },
      "label": "> [!definition] Definition · Representation of a Lie superalgebra",
      "context": {
        "range": [
          7966,
          8704
        ],
        "quote": "\n\n> [!definition] Definition · Representation of a Lie superalgebra\n>\n> A [<u class=\"concept-term\" data-concept-reference=\"concepts/representation-theory/lie-superalgebra-representation\" data-concept-identity=\"urn:uuid:c45f5876-ea6e-409e-b221-625213a50b9f\" data-concept-route=\"/concept-identities#concept-c45f5876-ea6e-409e-b221-625213a50b9f\">representation of a Lie superalgebra</u>](../../../../../concepts/representation-theory/lie-superalgebra-representation) is a homomorphism $\\Phi$ preserving the superbracket:\n>\n> $$\n> [\\Phi(X),\\Phi(Y)]_\\pm=\\Phi([X,Y]_\\pm).\n> $$\n>\n> It takes values in a Lie superalgebra of linear operators, with $|\\Phi(X)|=|X|$ and\n>\n> $$\n> [\\Phi(X),\\Phi(Y)]_\\pm=\\Phi(X)\\Phi(Y)-(-)^{|X||Y|}\\Phi(Y)\\Phi(X).\n> $$\n",
        "quote_sha256": "226f84df23ca631fb9d1c0b71a6711414c977b7a76318dc5b7f158515a58ff30",
        "environment": "definition",
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "books/woit-qtgr/2025-10-20/zh/chapter-31/01-quantization-of-pseudo-classical-systems",
          "lang": "zh-CN",
          "source_category": "machine_draft",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-a692dc0ff62d78964c88089c"
    },
    {
      "concept_id": "urn:uuid:c45f5876-ea6e-409e-b221-625213a50b9f",
      "book_id": "woit-qtgr",
      "edition_id": "2025-10-20",
      "lang": "en",
      "route": "books/woit-qtgr/2025-10-20/en/chapter-31/01-quantization-of-pseudo-classical-systems",
      "anchor": "first-b64fd7ba5ab4854767e5-en",
      "chapter": "31",
      "section": "31.1",
      "offset": 1026,
      "range": [
        8041,
        8349
      ],
      "source_revision": "323639751e7a7355386f87b2eada21802660b14be73d21d4f7d2491940c6fe64",
      "source_category": "machine_draft",
      "review_status": "machine-draft-not-reviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "explicit-source-uuid-marker"
      },
      "label": "representation of a Lie superalgebra",
      "context": {
        "range": [
          7966,
          8704
        ],
        "quote": "\n\n> [!definition] Definition · Representation of a Lie superalgebra\n>\n> A [<u class=\"concept-term\" data-concept-reference=\"concepts/representation-theory/lie-superalgebra-representation\" data-concept-identity=\"urn:uuid:c45f5876-ea6e-409e-b221-625213a50b9f\" data-concept-route=\"/concept-identities#concept-c45f5876-ea6e-409e-b221-625213a50b9f\">representation of a Lie superalgebra</u>](../../../../../concepts/representation-theory/lie-superalgebra-representation) is a homomorphism $\\Phi$ preserving the superbracket:\n>\n> $$\n> [\\Phi(X),\\Phi(Y)]_\\pm=\\Phi([X,Y]_\\pm).\n> $$\n>\n> It takes values in a Lie superalgebra of linear operators, with $|\\Phi(X)|=|X|$ and\n>\n> $$\n> [\\Phi(X),\\Phi(Y)]_\\pm=\\Phi(X)\\Phi(Y)-(-)^{|X||Y|}\\Phi(Y)\\Phi(X).\n> $$\n",
        "quote_sha256": "226f84df23ca631fb9d1c0b71a6711414c977b7a76318dc5b7f158515a58ff30",
        "environment": "definition",
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "books/woit-qtgr/2025-10-20/zh/chapter-31/01-quantization-of-pseudo-classical-systems",
          "lang": "zh-CN",
          "source_category": "machine_draft",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-f777edd063347f9190d32e8c"
    }
  ],
  "registered_positions": [
    {
      "route": "books/woit-qtgr/2025-10-20/en/chapter-31/01-quantization-of-pseudo-classical-systems",
      "lang": "en",
      "section": "31.1",
      "signal": "named-definition",
      "label": "Representation of a Lie superalgebra",
      "english": "Representation of a Lie superalgebra",
      "offset": 881
    },
    {
      "route": "books/woit-qtgr/2025-10-20/en/chapter-31/01-quantization-of-pseudo-classical-systems",
      "lang": "en",
      "section": "31.1",
      "signal": "term-mark",
      "label": "representation of a Lie superalgebra",
      "english": "representation of a Lie superalgebra",
      "offset": 955
    },
    {
      "route": "books/woit-qtgr/2025-10-20/zh/chapter-31/01-quantization-of-pseudo-classical-systems",
      "lang": "zh-CN",
      "section": "31.1",
      "signal": "term-mark",
      "label": "李超代数表示",
      "english": "representation of a Lie superalgebra",
      "offset": 488
    },
    {
      "route": "books/woit-qtgr/2025-10-20/zh/chapter-31/01-quantization-of-pseudo-classical-systems",
      "lang": "zh-CN",
      "section": "31.1",
      "signal": "named-definition",
      "label": "李超代数表示",
      "english": "",
      "offset": 454
    }
  ],
  "statements": [],
  "resolved_references": [],
  "reading_order": [
    "occ-06b026e350335315e330d4c3",
    "occ-b4888e470be538fb843d5a71",
    "occ-a692dc0ff62d78964c88089c",
    "occ-f777edd063347f9190d32e8c"
  ],
  "recorded_dependencies": [],
  "reading_paths": [],
  "coverage": {
    "registered_positions": 4,
    "located_occurrences": 4,
    "whole_book_search_complete": false,
    "registered_positions_truncated": false,
    "independent_human_review_implied": false
  },
  "unresolved": [],
  "base_revision": "a2c028a9d0e103f2581300cc34854517e5b23d60dd9d851163c181e0597081d6",
  "optional_enrichments": []
}