Viviane Ribeiro Tomaz da Silva

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 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.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.

On ℤp-graded identities and cocharacters of the Grassmann algebra

ABSTRACT Let p be an odd prime number, F a field of characteristic zero, and let Ebe the unitary Grassmann algebra generated by the infinite-dimensionalF-vector space L. We determine the bases of the ℤp-graded identities.Moreover we compute the ℤp-graded codimension and cocharacter sequences for the algebra E endowed with any ℤp-grading such that L is a homogeneous subspace.

A note on graded polynomial identities for tensor products by the Grassmann algebra in positive characteristic

Let G be a finite abelian group. As a consequence of the results of Di Vincenzo and Nardozza, we have that the generators of the TG-ideal of G-graded identities of a G-graded algebra in characteris...