Álgebra de Grassman: identidades polinomiais e polinômios centrais com involução.

Abstract

Let K be an infinite field of characteristic , 2, E is the infinite-dimensional Grassmann algebra over this field, and φ is an involution on E. Based primarily on [1], in this work, we present a description of the sets of ∗−polynomial identities, Id(E, φ), and the sets of ∗−central polynomials, C(E, φ), for the cases of characteristic 0 and characteristic p > 2. Furthermore, we show that if p > 2, then C(E, φ) is not finitely generated as a T(∗)-space.