Identities and central polynomials of real graded division algebras

TL;DR

This paper characterizes the graded identities and central polynomials of finite dimensional real division graded algebras, providing finite bases for these polynomial spaces.

Contribution

It offers the first finite basis descriptions for the $T_G$-ideal of graded identities and the $T_G$-space of graded central polynomials in this context.

Findings

Finite basis for graded identities of real division graded algebras.

Finite basis for graded central polynomials of these algebras.

Clarification of polynomial structure in real graded division algebras.

Abstract

Let $A$ be a finite dimensional real algebra with a division grading by a finite abelian group $G$. In this paper we provide finite basis for the $T_G$-ideal of graded identities and for the $T_G$-space of graded central polynomials for $A$.