Rota-Baxter operators of weight zero on Cayley-Dickson algebra

TL;DR

This paper classifies all Rota-Baxter operators of weight zero on split octonion algebras, completing the classification on composition algebras with detailed descriptions over different fields.

Contribution

It provides a complete classification of Rota-Baxter operators of weight zero on split octonion algebras, including explicit descriptions over various fields.

Findings

Classification up to conjugation by automorphisms and antiautomorphisms

Two descriptions: general over arbitrary fields and detailed over quadratically closed fields

Classification of Rota-Baxter operators on composition algebras is complete

Abstract

All Rota-Baxter operators of weight zero on split octonion algebra over a~field of characteristic not 2 are classified up to conjugation by automorphisms and antiautomorphisms. Thus, the classification of Rota-Baxter operators on composition algebras is finished. There are two descriptions: a~common description over arbitratry field of characteristic not 2 and more accurate description over a~quadratically closed field of characteristic not 2.