ℤ2 and ℤ-graded central polynomials of the Grassmann algebra

Abstract

Let [Formula: see text] be an infinite field of characteristic different from 2, and let [Formula: see text] be the Grassmann algebra of a countable of dimensional [Formula: see text]-vector space [Formula: see text]. In this paper, we study the graded central polynomials of gradings on [Formula: see text] by the groups [Formula: see text] and [Formula: see text], where the basis of the vector space [Formula: see text] is homogeneous. More specifically, we provide a basis for the [Formula: see text]-space of graded central polynomials for [Formula: see text], where the group [Formula: see text] is [Formula: see text] and [Formula: see text].