Classification of involutions on graded-division simple real algebras

TL;DR

This paper provides a comprehensive classification of involutions on graded-division simple real associative algebras with abelian grading groups, up to isomorphism and equivalence.

Contribution

It offers a complete classification of involutions on these algebras, extending understanding of their structure and symmetries.

Findings

Classification results for involutions on graded-division simple real algebras

Characterization of involutions up to isomorphism and equivalence

Framework applicable to algebras with abelian grading groups

Abstract

We classify, up to isomorphism and up to equivalence, involutions on graded-division finite-dimensional simple real (associative) algebras, when the grading group is abelian.