Identities and central polynomials with involution for the Grassmann algebra

Abstract

Let E be the infinite dimensional Grassmann algebra over an infinite field of characteristic p different from 2. Given an involution φ on E, denote by Id(E,φ) and C(E,φ) the set of all ⁎-polynomial identities and ⁎-central polynomials of (E,φ) respectively. In this paper we describe Id(E,φ) and C(E,φ). Moreover, we prove that C(E,φ) is not finitely generated as a T(⁎)-space if p>2.