Identities and central polynomials for real graded division algebras

Abstract

Let [Formula: see text] be a finite dimensional simple real algebra with a division grading by a finite abelian group [Formula: see text]. In this paper, we provide a finite basis for the [Formula: see text]-ideal of graded polynomial identities for [Formula: see text] and a finite basis for the [Formula: see text]-space of graded central polynomials for [Formula: see text].