"Lie algebra" meaning in English

{
  "etymology_text": "Named in honor of Sophus Lie (1842–1899), a Norwegian mathematician, in the 1930s by Hermann Weyl.",
  "forms": [
    {
      "form": "Lie algebras",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Lie algebra (plural Lie algebras)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
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          "name": "English entries with incorrect language header",
          "parents": [],
          "source": "w"
        },
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        },
        {
          "kind": "other",
          "name": "Serbo-Croatian terms with redundant script codes",
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        },
        {
          "kind": "other",
          "name": "Terms with Bulgarian translations",
          "parents": [],
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        {
          "kind": "other",
          "name": "Terms with Finnish translations",
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          "name": "Terms with German translations",
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        {
          "kind": "other",
          "name": "Terms with Japanese translations",
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        },
        {
          "kind": "other",
          "name": "Terms with Russian translations",
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          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Serbo-Croatian translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [],
          "source": "w"
        }
      ],
      "derived": [
        {
          "word": "Lie bialgebra"
        },
        {
          "word": "Lie coalgebra"
        },
        {
          "word": "Lie superalgebra"
        }
      ],
      "glosses": [
        "An algebra over a field whose bilinear product is alternating (or, equivalently for a bilinear product, anticommutative) and satisfies the Jacobi identity. Such a bilinear product is called a Lie bracket."
      ],
      "id": "en-Lie_algebra-en-noun-oMUaxd5A",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "algebra over a field",
          "algebra over a field"
        ],
        [
          "bilinear",
          "bilinear"
        ],
        [
          "product",
          "product"
        ],
        [
          "alternating",
          "alternating"
        ],
        [
          "anticommutative",
          "anticommutative"
        ],
        [
          "Jacobi identity",
          "Jacobi identity"
        ],
        [
          "Lie bracket",
          "Lie bracket"
        ]
      ],
      "raw_glosses": [
        "(mathematics) An algebra over a field whose bilinear product is alternating (or, equivalently for a bilinear product, anticommutative) and satisfies the Jacobi identity. Such a bilinear product is called a Lie bracket."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "code": "bg",
          "lang": "Bulgarian",
          "roman": "algebra na Li",
          "sense": "algebraic structure",
          "tags": [
            "feminine"
          ],
          "word": "алгебра на Ли"
        },
        {
          "code": "fi",
          "lang": "Finnish",
          "sense": "algebraic structure",
          "word": "Lien algebra"
        },
        {
          "code": "de",
          "lang": "German",
          "sense": "algebraic structure",
          "word": "Lie-Algebra"
        },
        {
          "code": "ja",
          "lang": "Japanese",
          "roman": "rīdaisū",
          "sense": "algebraic structure",
          "word": "リー代数"
        },
        {
          "code": "ru",
          "lang": "Russian",
          "roman": "álgebra Li",
          "sense": "algebraic structure",
          "tags": [
            "feminine"
          ],
          "word": "а́лгебра Ли"
        },
        {
          "code": "sh",
          "lang": "Serbo-Croatian",
          "sense": "algebraic structure",
          "tags": [
            "Roman",
            "feminine"
          ],
          "word": "Liejeva algebra"
        }
      ],
      "wikipedia": [
        "Hermann Weyl",
        "Lie algebra",
        "Sophus Lie"
      ]
    }
  ],
  "sounds": [
    {
      "ipa": "/liː.ældʒɨbɹə/"
    }
  ],
  "word": "Lie algebra"
}

{
  "derived": [
    {
      "word": "Lie bialgebra"
    },
    {
      "word": "Lie coalgebra"
    },
    {
      "word": "Lie superalgebra"
    }
  ],
  "etymology_text": "Named in honor of Sophus Lie (1842–1899), a Norwegian mathematician, in the 1930s by Hermann Weyl.",
  "forms": [
    {
      "form": "Lie algebras",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Lie algebra (plural Lie algebras)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
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        "English countable nouns",
        "English entries with incorrect language header",
        "English eponyms",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "Entries with translation boxes",
        "Pages with 1 entry",
        "Pages with entries",
        "Serbo-Croatian terms with redundant script codes",
        "Terms with Bulgarian translations",
        "Terms with Finnish translations",
        "Terms with German translations",
        "Terms with Japanese translations",
        "Terms with Russian translations",
        "Terms with Serbo-Croatian translations",
        "en:Mathematics"
      ],
      "glosses": [
        "An algebra over a field whose bilinear product is alternating (or, equivalently for a bilinear product, anticommutative) and satisfies the Jacobi identity. Such a bilinear product is called a Lie bracket."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "algebra over a field",
          "algebra over a field"
        ],
        [
          "bilinear",
          "bilinear"
        ],
        [
          "product",
          "product"
        ],
        [
          "alternating",
          "alternating"
        ],
        [
          "anticommutative",
          "anticommutative"
        ],
        [
          "Jacobi identity",
          "Jacobi identity"
        ],
        [
          "Lie bracket",
          "Lie bracket"
        ]
      ],
      "raw_glosses": [
        "(mathematics) An algebra over a field whose bilinear product is alternating (or, equivalently for a bilinear product, anticommutative) and satisfies the Jacobi identity. Such a bilinear product is called a Lie bracket."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Hermann Weyl",
        "Lie algebra",
        "Sophus Lie"
      ]
    }
  ],
  "sounds": [
    {
      "ipa": "/liː.ældʒɨbɹə/"
    }
  ],
  "translations": [
    {
      "code": "bg",
      "lang": "Bulgarian",
      "roman": "algebra na Li",
      "sense": "algebraic structure",
      "tags": [
        "feminine"
      ],
      "word": "алгебра на Ли"
    },
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "algebraic structure",
      "word": "Lien algebra"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "algebraic structure",
      "word": "Lie-Algebra"
    },
    {
      "code": "ja",
      "lang": "Japanese",
      "roman": "rīdaisū",
      "sense": "algebraic structure",
      "word": "リー代数"
    },
    {
      "code": "ru",
      "lang": "Russian",
      "roman": "álgebra Li",
      "sense": "algebraic structure",
      "tags": [
        "feminine"
      ],
      "word": "а́лгебра Ли"
    },
    {
      "code": "sh",
      "lang": "Serbo-Croatian",
      "sense": "algebraic structure",
      "tags": [
        "Roman",
        "feminine"
      ],
      "word": "Liejeva algebra"
    }
  ],
  "word": "Lie algebra"
}