See Clifford algebra on Wiktionary
{
"etymology_text": "Named after William Kingdon Clifford (1845–1879), an English mathematician and philosopher.",
"forms": [
{
"form": "Clifford algebras",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "Clifford algebra (plural Clifford algebras)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
{
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w"
},
{
"kind": "other",
"name": "Entries with translation boxes",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Pages with 1 entry",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Pages with entries",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with French translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with German translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Italian translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Japanese translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Korean translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Mandarin translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Portuguese translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Russian translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Spanish translations",
"parents": [],
"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Algebra",
"orig": "en:Algebra",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
}
],
"glosses": [
"A unital associative algebra which generalizes the algebra of quaternions but which is not necessarily a division algebra; it is generated by a set of γᵢ (with i ranging from, say, 1 to n) such that the square of each γᵢ is fixed to be either +1 or −1, depending on each i, and such that any product γᵢγⱼ anticommutes when its factors are distinct (i.e., when i ne j)."
],
"hypernyms": [
{
"word": "filtered algebra"
}
],
"id": "en-Clifford_algebra-en-noun-Bd-go2pP",
"links": [
[
"algebra",
"algebra"
],
[
"unital",
"unital"
],
[
"associative algebra",
"associative algebra"
],
[
"quaternion",
"quaternion"
],
[
"division algebra",
"division algebra"
],
[
"anticommute",
"anticommute"
]
],
"qualifier": "mathematical physics",
"raw_glosses": [
"(algebra, mathematical physics) A unital associative algebra which generalizes the algebra of quaternions but which is not necessarily a division algebra; it is generated by a set of γᵢ (with i ranging from, say, 1 to n) such that the square of each γᵢ is fixed to be either +1 or −1, depending on each i, and such that any product γᵢγⱼ anticommutes when its factors are distinct (i.e., when i ne j)."
],
"topics": [
"algebra",
"mathematics",
"sciences"
],
"translations": [
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "Kèlìfúdé dàishù",
"sense": "unital associative algebra which generalizes the algebra of quaternions",
"word": "克利福德代数"
},
{
"code": "fr",
"lang": "French",
"sense": "unital associative algebra which generalizes the algebra of quaternions",
"tags": [
"feminine"
],
"word": "algèbre de Clifford"
},
{
"code": "de",
"lang": "German",
"sense": "unital associative algebra which generalizes the algebra of quaternions",
"tags": [
"feminine"
],
"word": "Clifford-Algebra"
},
{
"code": "it",
"lang": "Italian",
"sense": "unital associative algebra which generalizes the algebra of quaternions",
"tags": [
"feminine"
],
"word": "algebra di Clifford"
},
{
"code": "ja",
"lang": "Japanese",
"roman": "Kurifōdo-daisū",
"sense": "unital associative algebra which generalizes the algebra of quaternions",
"word": "クリフォード代数"
},
{
"code": "ko",
"lang": "Korean",
"roman": "Keullipeodeu daesu",
"sense": "unital associative algebra which generalizes the algebra of quaternions",
"word": "클리퍼드 대수"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "unital associative algebra which generalizes the algebra of quaternions",
"tags": [
"feminine"
],
"word": "álgebra de Clifford"
},
{
"code": "ru",
"english": "algebra Klifforda",
"lang": "Russian",
"sense": "unital associative algebra which generalizes the algebra of quaternions",
"tags": [
"feminine"
],
"word": "алгебра Клиффорда"
},
{
"code": "es",
"lang": "Spanish",
"sense": "unital associative algebra which generalizes the algebra of quaternions",
"word": "álgebra de Clifford"
}
],
"wikipedia": [
"Clifford algebra",
"William Kingdon Clifford"
]
}
],
"word": "Clifford algebra"
}
{
"etymology_text": "Named after William Kingdon Clifford (1845–1879), an English mathematician and philosopher.",
"forms": [
{
"form": "Clifford algebras",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "Clifford algebra (plural Clifford algebras)",
"name": "en-noun"
}
],
"hypernyms": [
{
"word": "filtered algebra"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
"English countable nouns",
"English entries with incorrect language header",
"English lemmas",
"English multiword terms",
"English nouns",
"Entries with translation boxes",
"Pages with 1 entry",
"Pages with entries",
"Terms with French translations",
"Terms with German translations",
"Terms with Italian translations",
"Terms with Japanese translations",
"Terms with Korean translations",
"Terms with Mandarin translations",
"Terms with Portuguese translations",
"Terms with Russian translations",
"Terms with Spanish translations",
"en:Algebra"
],
"glosses": [
"A unital associative algebra which generalizes the algebra of quaternions but which is not necessarily a division algebra; it is generated by a set of γᵢ (with i ranging from, say, 1 to n) such that the square of each γᵢ is fixed to be either +1 or −1, depending on each i, and such that any product γᵢγⱼ anticommutes when its factors are distinct (i.e., when i ne j)."
],
"links": [
[
"algebra",
"algebra"
],
[
"unital",
"unital"
],
[
"associative algebra",
"associative algebra"
],
[
"quaternion",
"quaternion"
],
[
"division algebra",
"division algebra"
],
[
"anticommute",
"anticommute"
]
],
"qualifier": "mathematical physics",
"raw_glosses": [
"(algebra, mathematical physics) A unital associative algebra which generalizes the algebra of quaternions but which is not necessarily a division algebra; it is generated by a set of γᵢ (with i ranging from, say, 1 to n) such that the square of each γᵢ is fixed to be either +1 or −1, depending on each i, and such that any product γᵢγⱼ anticommutes when its factors are distinct (i.e., when i ne j)."
],
"topics": [
"algebra",
"mathematics",
"sciences"
],
"wikipedia": [
"Clifford algebra",
"William Kingdon Clifford"
]
}
],
"translations": [
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "Kèlìfúdé dàishù",
"sense": "unital associative algebra which generalizes the algebra of quaternions",
"word": "克利福德代数"
},
{
"code": "fr",
"lang": "French",
"sense": "unital associative algebra which generalizes the algebra of quaternions",
"tags": [
"feminine"
],
"word": "algèbre de Clifford"
},
{
"code": "de",
"lang": "German",
"sense": "unital associative algebra which generalizes the algebra of quaternions",
"tags": [
"feminine"
],
"word": "Clifford-Algebra"
},
{
"code": "it",
"lang": "Italian",
"sense": "unital associative algebra which generalizes the algebra of quaternions",
"tags": [
"feminine"
],
"word": "algebra di Clifford"
},
{
"code": "ja",
"lang": "Japanese",
"roman": "Kurifōdo-daisū",
"sense": "unital associative algebra which generalizes the algebra of quaternions",
"word": "クリフォード代数"
},
{
"code": "ko",
"lang": "Korean",
"roman": "Keullipeodeu daesu",
"sense": "unital associative algebra which generalizes the algebra of quaternions",
"word": "클리퍼드 대수"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "unital associative algebra which generalizes the algebra of quaternions",
"tags": [
"feminine"
],
"word": "álgebra de Clifford"
},
{
"code": "ru",
"english": "algebra Klifforda",
"lang": "Russian",
"sense": "unital associative algebra which generalizes the algebra of quaternions",
"tags": [
"feminine"
],
"word": "алгебра Клиффорда"
},
{
"code": "es",
"lang": "Spanish",
"sense": "unital associative algebra which generalizes the algebra of quaternions",
"word": "álgebra de Clifford"
}
],
"word": "Clifford algebra"
}
Download raw JSONL data for Clifford algebra meaning in All languages combined (3.7kB)
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.
If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.