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].

$\mathbb{Z}$-gradings of full support on the Grassmann algebra

“…In [13,16] the authors studied three types of Z-grading on E, which were denoted by E ∞ , E k * and E k , for all non-negative integer k. These structures are the more natural Z-grading on E due to its closely relation with the superalgebras E ∞ , E k * and E k . The support of E k * is {0, 1, .…”