TY - JOUR

T1 - Rota-Baxter Operators of Weight Zero on CayleyDickson Algebra with Matrix Images

AU - Panasenko, Alexander S.

N1 - Panasenko A. S. Rota-Baxter Operators of Weight Zero on Cayley-Dickson Algebra with Matrix Images. The Bulletin of Irkutsk State University. Series Mathematics, 2025, vol. 54, pp. 113–128. https://doi.org/10.26516/1997-7670.2025.54.113 The study was supported by a grant from the Russian Science Foundation № 23-71-10005, https://rscf.ru/project/23-71-10005/ The author is very grateful to V. Yu. Gubarev for his advices in Rota-Baxter theory.

PY - 2025

Y1 - 2025

N2 - Rota-Baxter operators present a natural generalization of integration byparts 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 automorphismsand antiautomorphisms of octonions.

AB - Rota-Baxter operators present a natural generalization of integration byparts 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 automorphismsand antiautomorphisms of octonions.

KW - Cayley-Dickson algebra

KW - Rota-Baxter operator

KW - split octonions

KW - automorphism

KW - antiautomorphism

UR - https://www.scopus.com/pages/publications/105023993282

U2 - 10.26516/1997-7670.2025.54.113

DO - 10.26516/1997-7670.2025.54.113

M3 - Article

VL - 54

SP - 113

EP - 128

JO - Bulletin of Irkutsk State University, Series Mathematics

JF - Bulletin of Irkutsk State University, Series Mathematics

SN - 1997-7670

ER -