Clifford algebra

English

Etymology

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

Noun

Clifford algebra (plural Clifford algebras)

1. (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 $\gamma _{i}$ (with i ranging from, say, 1 to n) such that the square of each $\gamma _{i}$ is fixed to be either +1 or −1, depending on each i, and such that any product $\gamma _{i}\gamma _{j}$ anticommutes when its factors are distinct (i.e., when $i\neq j$).

Hypernyms

• filtered algebra

Translations

unital associative algebra which generalizes the algebra of quaternions

• Chinese:

  Mandarin: 克利福德代数 (Kèlìfúdé dàishù)

• French: algèbre de Clifford f
• German: Clifford-Algebra f
• Italian: algebra di Clifford f
• Japanese: クリフォード代数 (Kurifōdo-daisū)
• Korean: 클리퍼드 대수 (Keullipeodeu daesu)
• Portuguese: álgebra de Clifford f
• Russian: алгебра Клиффорда f (algebra Klifforda)
• Spanish: álgebra de Clifford