Wedge Products of Alternating Forms

Let V be a vector space of dimension d < ∞. In these notes, we discuss how to define a wedge product on the space of all alternating forms on V × · · · × V ’s so as to make it isomorphic to the exterior algebra Λ(V ). We start by reviewing the equivalence class definition of the exterior algebra over the dual space V ∗ of V . Define ◦ C(V ) = ⊕∞ k=0 V ∗⊗k (with V ∗⊗k being the tensor product of k copies of V ∗ when k > 0 and being IR when k = 0) and ◦ let I(V ) be the two–sided ideal in C(V ) generated by {