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Rota-Baxter Operators of Nonzero Weight on the Split Octonions. / Panasenko, A. S.

In: Advances in Applied Clifford Algebras, Vol. 35, No. 3, 27, 24.05.2025.

Research output: Contribution to journal › Article › peer-review

Harvard

Panasenko, AS 2025, 'Rota-Baxter Operators of Nonzero Weight on the Split Octonions', Advances in Applied Clifford Algebras, vol. 35, no. 3, 27. https://doi.org/10.1007/s00006-025-01389-4

APA

Panasenko, A. S. (2025). Rota-Baxter Operators of Nonzero Weight on the Split Octonions. Advances in Applied Clifford Algebras, 35(3), [27]. https://doi.org/10.1007/s00006-025-01389-4

Vancouver

Panasenko AS. Rota-Baxter Operators of Nonzero Weight on the Split Octonions. Advances in Applied Clifford Algebras. 2025 May 24;35(3):27. doi: 10.1007/s00006-025-01389-4

Author

Panasenko, A. S. / Rota-Baxter Operators of Nonzero Weight on the Split Octonions. In: Advances in Applied Clifford Algebras. 2025 ; Vol. 35, No. 3.

BibTeX

@article{4d6edfbcedb0419182a8f09ec174fee6,
title = "Rota-Baxter Operators of Nonzero Weight on the Split Octonions",
abstract = "We describe Rota-Baxter operators on split octonions. It turns out that up to some transformations there exists exactly one such non-splitting operator over any field. We also obtain a description of all decompositions of split octonions over a quadratically closed field of characteristic different from 2 into a sum of two subalgebras, which describes the splitting Rota-Baxter operators. It completes the classification of Rota-Baxter operators on composition algebras of any weight.",
keywords = "Antiautomorphism, Automorphism, Cayley-Dickson algebra, Rota-Baxter operator, Split octonions",
author = "Panasenko, {A. S.}",
note = "The author expresses gratitude to V. Yu. Gubarev for useful discussions. The study was supported by a grant from the Russian Science Foundation No 23-71-10005, https://rscf.ru/project/23-71-10005/.",
year = "2025",
month = may,
day = "24",
doi = "10.1007/s00006-025-01389-4",
language = "English",
volume = "35",
journal = "Advances in Applied Clifford Algebras",
issn = "1661-4909",
publisher = "Springer Nature",
number = "3",

}

RIS

TY - JOUR

T1 - Rota-Baxter Operators of Nonzero Weight on the Split Octonions

AU - Panasenko, A. S.

N1 - The author expresses gratitude to V. Yu. Gubarev for useful discussions. The study was supported by a grant from the Russian Science Foundation No 23-71-10005, https://rscf.ru/project/23-71-10005/.

PY - 2025/5/24

Y1 - 2025/5/24

N2 - We describe Rota-Baxter operators on split octonions. It turns out that up to some transformations there exists exactly one such non-splitting operator over any field. We also obtain a description of all decompositions of split octonions over a quadratically closed field of characteristic different from 2 into a sum of two subalgebras, which describes the splitting Rota-Baxter operators. It completes the classification of Rota-Baxter operators on composition algebras of any weight.

AB - We describe Rota-Baxter operators on split octonions. It turns out that up to some transformations there exists exactly one such non-splitting operator over any field. We also obtain a description of all decompositions of split octonions over a quadratically closed field of characteristic different from 2 into a sum of two subalgebras, which describes the splitting Rota-Baxter operators. It completes the classification of Rota-Baxter operators on composition algebras of any weight.

KW - Antiautomorphism

KW - Automorphism

KW - Cayley-Dickson algebra

KW - Rota-Baxter operator

KW - Split octonions

UR - https://www.mendeley.com/catalogue/2e41402a-de1b-3f2f-9abe-901ff92fae20/

U2 - 10.1007/s00006-025-01389-4

DO - 10.1007/s00006-025-01389-4

M3 - Article

VL - 35

JO - Advances in Applied Clifford Algebras

JF - Advances in Applied Clifford Algebras

SN - 1661-4909

IS - 3

M1 - 27

ER -

ID: 67077427