A Grassmann algebra
(also known as an exterior algebra
) is a unital associative algebra
by a set, S subject to the relation χξ+ξχ=0 for any χ,ξ in S. This definition amounts to saying that the generators are anti-commuting quantities (and otherwise 'as general as possible); it should be modified in case K has characteristic
The construction of such an algebra comes from the wedge product: take the vector space V that has S as basis, and the direct sum of all the exterior powers of V, using wedge product in each graded piece. If S is finite of cardinality n, the Grassmann algebra has as basis one wedge product for each subset of S, and each product made up by wedging elements of S with repeats is equal to 0.
See Fermion, Supersymmetry, Superspace, Superalgebra, Supergroup, Hermann Grassmann, p-form, Berezin integral
This article is a stub. You can help Wikipedia by fixing it.