Cayley–Dickson construction
In mathematics, the Cayley–Dickson construction, named after Arthur Cayley and Leonard Eugene Dickson, produces a sequence of algebras over the field of real numbers, each with twice the dimension of the previous one. The algebras produced by this process are known as Cayley–Dickson algebras. They are useful composition algebras frequently applied in mathematical physics. The symmetries of the real field disappear as the Cayley–Dickson construction is repeatedly applied: first losing order, then commutativity of multiplication, and next associativity of multiplication.
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Cayley–Dickson construction
In mathematics, the Cayley–Dickson construction, named after Arthur Cayley and Leonard Eugene Dickson, produces a sequence of algebras over the field of real numbers, each with twice the dimension of the previous one. The algebras produced by this process are known as Cayley–Dickson algebras. They are useful composition algebras frequently applied in mathematical physics. The symmetries of the real field disappear as the Cayley–Dickson construction is repeatedly applied: first losing order, then commutativity of multiplication, and next associativity of multiplication.
has abstract
Das Verdopplungsverfahren, auc ...... d die Sedenionen hervorbringt.
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En matemáticas, la construcció ...... opiedad algebraica específica.
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In de wiskunde produceert de C ...... utie met tweemaal de dimensie.
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In matematica, la costruzione ...... pre commutativa e associativa.
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In mathematics, the Cayley–Dic ...... lution of twice the dimension.
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Процедура Кэли — Диксона (проц ...... рмированных алгебр с делением.
@ru
在数系理论中，凯莱-迪克森构造以定义在实数集的代数结构为基础 ...... 个更高的维度数之外，都将失去前一个系统所拥有的一个特定性质。
@zh
数学におけるケーリー＝ディクソンの構成法（ケーリー・ディクソ ...... つき代数系をとって倍の次元の対合つき代数系にすることである。
@ja
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Das Verdopplungsverfahren, auc ...... d die Sedenionen hervorbringt.
@de
En matemáticas, la construcció ...... a ser el cuadrado de su norma.
@es
In de wiskunde produceert de C ...... utie met tweemaal de dimensie.
@nl
In matematica, la costruzione ...... pre commutativa e associativa.
@it
In mathematics, the Cayley–Dic ...... sociativity of multiplication.
@en
Процедура Кэли — Диксона (проц ...... рмированных алгебр с делением.
@ru
在数系理论中，凯莱-迪克森构造以定义在实数集的代数结构为基础 ...... 个更高的维度数之外，都将失去前一个系统所拥有的一个特定性质。
@zh
数学におけるケーリー＝ディクソンの構成法（ケーリー・ディクソ ...... つき代数系をとって倍の次元の対合つき代数系にすることである。
@ja
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Cayley-Dickson-constructie
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Cayley–Dickson construction
@en
Construcción de Cayley-Dickson
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Costruzione di Cayley-Dickson
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Verdopplungsverfahren
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Процедура Кэли — Диксона
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ケーリー＝ディクソンの構成法
@ja
凯莱-迪克森结构
@zh