On Z2-graded polynomial identities of the Grassmann algebra

Let F be a field of characteristic zero and let E be the Grassmann algebra of an infinite dimensional F-vector space L. In this paper we study the Z2-graded polynomial identities of E with respect to any fixed Z2-grading such that L is an homogeneous subspace. We found explicit generators for the ideal, T2(E), of graded polynomial identities of E and we determine its cocharacter and codimension sequences.