Clifford algebras

Grading

Clifford algebras are Z₂-graded algebras (also known as superalgebras). Indeed, the linear map on V defined by v ↦ −v (reflection through the origin) preserves the quadratic form Q and so by the universal property of Clifford algebras extends to an algebra automorphism$${\displaystyle \alpha :\operatorname {Cl} (V,Q)\to \operatorname {Cl} (V,Q).}$$