The Weil Algebra

Abstract

Let V be an n-dimensional vector space, and let ⋀ = ⋀(V) be the exterior algebra of V considered as a commutative superalgebra, and let S = S(V) be the symmetric algebra considered as an algebra all of whose elements are even. So we assign to each element of ⋀V its exterior degree, but each element of S ^k (V) is assigned the degree 2k. The Koszul algebra is the tensor product ⋀ ⊗S.