Identidades e polinômios centrais graduados para o produto tensorial pela álgebra de Grassmann.

Abstract

LetG be an abelian group andR aG-graded algebra. We consider in the tensor product R ⊗ E, where E is the exterior algebra of infinite dimension, the natural (G×Z2)-grading, obtained fromG-grading ofR. In this work, we present results that relates the graded identities and also relates the graded central polynomials of the algebrasR andR⊗E. As an application we obtain the PI-equivalence between the algebras M1,1(E)⊗E and M2(E), which is a part of the Tensor Product Theorem of Kemer. We also present descriptions of the (Zn × Z2)-graded identities and central polynomials of the algebra Mn(E), as well as of theZ2-graded identities and central polynomials of the algebra E ⊗ E. In the last case, we consider a different grading from the usual one.