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

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.