ℤ₂-Codimensions of the Grassmann Algebra

Abstract

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 ϕ _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 ϕ _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 ϕ-codimensions for a large amount of arbitrary automorphisms ϕ of E of order 2.

Key Words:

• Graded codimensions
• Grassmann algebra

2000 Mathematics Subject Classification:

• Primary 16R10
• Secondary 16P90

ACKNOWLEDGMENTS

I would like to thank Prof. Ana Cristina Vieira for useful comments.

Notes

Communicated by I. Shestakov.