See Clifford algebra in All languages combined, or Wiktionary
Download JSON data for Clifford algebra meaning in English (3.6kB)
{
"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": [
{
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{
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
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"Entry maintenance"
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{
"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"
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[
"quaternion",
"quaternion"
],
[
"division algebra",
"division algebra"
],
[
"anticommute",
"anticommute"
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"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"
]
}
],
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"args": {},
"expansion": "Clifford algebra (plural Clifford algebras)",
"name": "en-noun"
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}
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"lang": "English",
"lang_code": "en",
"pos": "noun",
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{
"categories": [
"English countable nouns",
"English entries with incorrect language header",
"English lemmas",
"English multiword terms",
"English nouns",
"en:Algebra"
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"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"
}
This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-03 from the enwiktionary dump dated 2024-05-02 using wiktextract (f4fd8c9 and c9440ce). 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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