Z2-CODIMENSIONS OF THE GRASSMANN ALGEBRA

Let E be the infinite-dimensional Grassmann algebra over a field F of characteristic zero, and consider L the F-vector space spanned by all generators of E. Let phi(l) be any fixed automorphism of E of order 2 such that L is an homogeneous subspace. Our goal is to finish the computation of the sequences of phi(l)-codimensions, by finding its exact value for the unique open case, that is, when the subspace of L corresponding to the eigenvalue 1 is finite-dimensional. As a consequence we get the phi-codimensions for a large amount of arbitrary automorphisms phi of E of order 2.