Clifford algebra

noun

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).

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Meanings

nounClifford algebra (plural Clifford algebras)

plural Clifford algebras

  1. mathematical physicsalgebraA 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).

Origin

Named after William Kingdon Clifford (1845–1879), an English mathematician and philosopher.

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Translations

Chinese Mandarin 克利福德代数
  • 克利福德代数 (Kèlìfúdé dàishù)unital associative algebra which generalizes the algebra of quaternions
French algèbre de Clifford
  • algèbre de Cliffordunital associative algebra which generalizes the algebra of quaternions
German Clifford-Algebra
  • Clifford-Algebraunital associative algebra which generalizes the algebra of quaternions
Italian algebra di Clifford
  • algebra di Cliffordunital associative algebra which generalizes the algebra of quaternions
Japanese クリフォード代数
  • クリフォード代数 (Kurifōdo-daisū)unital associative algebra which generalizes the algebra of quaternions
Korean 클리퍼드 대수
  • 클리퍼드 대수 (Keullipeodeu daesu)unital associative algebra which generalizes the algebra of quaternions
Portuguese álgebra de Clifford
  • álgebra de Cliffordunital associative algebra which generalizes the algebra of quaternions
Russian алгебра Клиффорда
  • алгебра Клиффордаunital associative algebra which generalizes the algebra of quaternions
Spanish álgebra de Clifford
  • álgebra de Cliffordunital associative algebra which generalizes the algebra of quaternions
Cite this entry
APA

Clifford algebra. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/Clifford%20algebra

MLA

“Clifford algebra.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Clifford%20algebra. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “Clifford algebra,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/Clifford%20algebra.

Source: Clifford algebra on Wiktionary, CC BY-SA 4.0.