"Möbius group" meaning in All languages combined

See Möbius group on Wiktionary

Noun [English]

Forms: Möbius groups [plural]
Etymology: Eponymous for August Ferdinand Möbius (1790–1868), a German mathematician and theoretical astronomer. Head templates: {{en-noun}} Möbius group (plural Möbius groups)
  1. (group theory) The projective general linear group mathbf PGL(2,ℂ): the group of Möbius transformations on the Riemann sphere. Categories (topical): Group theory Translations (PGL(2,C)): Möbius-groep [feminine, masculine] (Dutch), grupo de Möbius [masculine] (Spanish)
    Sense id: en-Möbius_group-en-noun-J0is7NYn Categories (other): English entries with incorrect language header, Entries with translation boxes, Pages with 1 entry, Pages with entries, Terms with Dutch translations, Terms with Spanish translations, Non-Euclidean geometry Disambiguation of English entries with incorrect language header: 67 33 Disambiguation of Entries with translation boxes: 82 18 Disambiguation of Pages with 1 entry: 69 31 Disambiguation of Pages with entries: 77 23 Disambiguation of Terms with Dutch translations: 71 29 Disambiguation of Terms with Spanish translations: 76 24 Disambiguation of Non-Euclidean geometry: 64 36 Topics: group-theory, mathematics, sciences Disambiguation of 'PGL(2,C)': 94 6
  2. (group theory) For a given dimension n, the group of projective transformations leaving a particular hypersphere invariant. Categories (topical): Group theory
    Sense id: en-Möbius_group-en-noun-ohRFK8Nm Topics: group-theory, mathematics, sciences
The following are not (yet) sense-disambiguated
Synonyms: Moebius group, Mobius group Hypernyms: Lie group Meronyms: Möbius transformation Related terms: Möbius strip, Möbius transformation

Inflected forms

{
  "etymology_text": "Eponymous for August Ferdinand Möbius (1790–1868), a German mathematician and theoretical astronomer.",
  "forms": [
    {
      "form": "Möbius groups",
      "tags": [
        "plural"
      ]
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  ],
  "head_templates": [
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      "args": {},
      "expansion": "Möbius group (plural Möbius groups)",
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    {
      "_dis1": "52 48",
      "word": "Lie group"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "meronyms": [
    {
      "_dis1": "52 48",
      "word": "Möbius transformation"
    }
  ],
  "pos": "noun",
  "related": [
    {
      "_dis1": "52 48",
      "word": "Möbius strip"
    },
    {
      "_dis1": "52 48",
      "word": "Möbius transformation"
    }
  ],
  "senses": [
    {
      "categories": [
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Group theory",
          "orig": "en:Group theory",
          "parents": [
            "Algebra",
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
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          "source": "w"
        },
        {
          "_dis": "67 33",
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            "Entry maintenance"
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          "source": "w+disamb"
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          "_dis": "82 18",
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          "name": "Non-Euclidean geometry",
          "orig": "en:Non-Euclidean geometry",
          "parents": [],
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      ],
      "glosses": [
        "The projective general linear group mathbf PGL(2,ℂ): the group of Möbius transformations on the Riemann sphere."
      ],
      "id": "en-Möbius_group-en-noun-J0is7NYn",
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        [
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          "Möbius transformations"
        ],
        [
          "Riemann sphere",
          "Riemann sphere"
        ]
      ],
      "raw_glosses": [
        "(group theory) The projective general linear group mathbf PGL(2,ℂ): the group of Möbius transformations on the Riemann sphere."
      ],
      "topics": [
        "group-theory",
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "_dis1": "94 6",
          "code": "nl",
          "lang": "Dutch",
          "sense": "PGL(2,C)",
          "tags": [
            "feminine",
            "masculine"
          ],
          "word": "Möbius-groep"
        },
        {
          "_dis1": "94 6",
          "code": "es",
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          "sense": "PGL(2,C)",
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            "masculine"
          ],
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        }
      ]
    },
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            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "For a given dimension n, the group of projective transformations leaving a particular hypersphere invariant."
      ],
      "id": "en-Möbius_group-en-noun-ohRFK8Nm",
      "links": [
        [
          "group theory",
          "group theory"
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        [
          "group",
          "group"
        ],
        [
          "hypersphere",
          "hypersphere"
        ],
        [
          "invariant",
          "invariant"
        ]
      ],
      "raw_glosses": [
        "(group theory) For a given dimension n, the group of projective transformations leaving a particular hypersphere invariant."
      ],
      "topics": [
        "group-theory",
        "mathematics",
        "sciences"
      ]
    }
  ],
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    {
      "_dis1": "52 48",
      "word": "Moebius group"
    },
    {
      "_dis1": "52 48",
      "word": "Mobius group"
    }
  ],
  "wikipedia": [
    "Möbius group"
  ],
  "word": "Möbius group"
}
{
  "categories": [
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    "English entries with incorrect language header",
    "English eponyms",
    "English lemmas",
    "English multiword terms",
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    "English terms spelled with ◌̈",
    "Entries with translation boxes",
    "Pages with 1 entry",
    "Pages with entries",
    "Terms with Dutch translations",
    "Terms with Spanish translations",
    "en:Non-Euclidean geometry"
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  "etymology_text": "Eponymous for August Ferdinand Möbius (1790–1868), a German mathematician and theoretical astronomer.",
  "forms": [
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      "tags": [
        "plural"
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      "word": "Lie group"
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  ],
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  "lang_code": "en",
  "meronyms": [
    {
      "word": "Möbius transformation"
    }
  ],
  "pos": "noun",
  "related": [
    {
      "word": "Möbius strip"
    },
    {
      "word": "Möbius transformation"
    }
  ],
  "senses": [
    {
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        "en:Group theory"
      ],
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        "The projective general linear group mathbf PGL(2,ℂ): the group of Möbius transformations on the Riemann sphere."
      ],
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        [
          "group theory",
          "group theory"
        ],
        [
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        ]
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        "(group theory) The projective general linear group mathbf PGL(2,ℂ): the group of Möbius transformations on the Riemann sphere."
      ],
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        "group-theory",
        "mathematics",
        "sciences"
      ]
    },
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      ],
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      ],
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        ],
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        ],
        [
          "invariant",
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        ]
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        "(group theory) For a given dimension n, the group of projective transformations leaving a particular hypersphere invariant."
      ],
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        "group-theory",
        "mathematics",
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      ]
    }
  ],
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    {
      "word": "Moebius group"
    },
    {
      "word": "Mobius group"
    }
  ],
  "translations": [
    {
      "code": "nl",
      "lang": "Dutch",
      "sense": "PGL(2,C)",
      "tags": [
        "feminine",
        "masculine"
      ],
      "word": "Möbius-groep"
    },
    {
      "code": "es",
      "lang": "Spanish",
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      "tags": [
        "masculine"
      ],
      "word": "grupo de Möbius"
    }
  ],
  "wikipedia": [
    "Möbius group"
  ],
  "word": "Möbius group"
}

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This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-12-21 from the enwiktionary dump dated 2024-12-04 using wiktextract (d8cb2f3 and 4e554ae). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

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