Simple Graded Division Algebras over the Field of Real Numbers

TL;DR

This paper classifies all finite-dimensional simple graded division algebras over the real numbers with any finite abelian group grading, providing a comprehensive understanding of their structure.

Contribution

It offers a complete classification of simple graded division algebras over the reals for all finite abelian grading groups, a problem previously unresolved.

Findings

Complete classification of simple graded division algebras over reals

Includes all finite abelian grading groups

Provides explicit descriptions of algebra structures

Abstract

We classify, up to equivalence, all finite-dimensional simple graded division algebras over the field of real numbers. The grading group is any finite abelian group.