Clifford algebra

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

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

• filtered algebra