Algebraic and logical methods in computer science and artificial intelligence

Rota-Baxter operators of weight zero on Cayley-Dickson algebra with matrix images

A. S. Panasenko<sup>ab

a</sup> Sobolev Institute of Mathematics SB RAS, Novosibirsk, Russian Federation
^b Novosibirsk State University, Novosibirsk, Russian Federation

Abstract: Rota-Baxter operators present a natural generalization of integration by parts formula for the integral operator. We consider Rota-Baxter operators of weight zero on split octonion algebra over a field of characteristic not 2. We classify all these operators under a condition of embeddability of their images in second order matrix algebra. With the additional condition of quadratic closure of the field, we obtain 9 operators. In addition, we refine the classification of Rota-Baxter operators on the second order matrix algebra by removing the restriction on the algebraic closure of the field. Classifications were obtained up to multiplication by a scalar, conjugation by automorphisms and antiautomorphisms. In particular, we constructed some automorphisms and antiautomorphisms of octonions.

Keywords: Cayley-Dickson algebra, Rota-Baxter operator, split octonions, automorphism, antiautomorphism.

UDC: 512.554.5

MSC: 17D05 , 17A36

Received: 12.02.2025
Revised: 26.03.2025
Accepted: 27.03.2025

Language: English

DOI: 10.26516/1997-7670.2025.54.113