Editing Clifford algebra (section)

=== As a quantization of the exterior algebra ===
Clifford algebras are closely related to [[exterior algebra]]s. Indeed, if {{math|1=''Q'' = 0}} then the Clifford algebra {{math|Cl(''V'', ''Q'')}} is just the exterior algebra {{math|⋀''V''}}. Whenever {{math|2}} is invertible in the ground field&nbsp;{{math|''K''}}, there exists a canonical ''linear'' isomorphism between {{math|⋀''V''}} and {{math|Cl(''V'', ''Q'')}}. That is, they are [[naturally isomorphic]] as vector spaces, but with different multiplications (in the case of characteristic two, they are still isomorphic as vector spaces, just not naturally). Clifford multiplication together with the distinguished subspace is strictly richer than the [[exterior product]] since it makes use of the extra information provided by&nbsp;{{math|''Q''}}.

The Clifford algebra is a [[filtered algebra]]; the [[associated graded algebra]] is the exterior algebra.

More precisely, Clifford algebras may be thought of as ''quantizations'' (cf. [[quantum group]]) of the exterior algebra, in the same way that the [[Weyl algebra]] is a quantization of the [[symmetric algebra]].

Weyl algebras and Clifford algebras admit a further structure of a [[*-algebra]], and can be unified as even and odd terms of a [[superalgebra]], as discussed in [[CCR and CAR algebras]].