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Rota—Baxter operators on the simple Jordan algebra of matrices of order two. / Gubarev, Vsevolod; Panasenko, Alexander.

In: Bulletin of the Malaysian Mathematical Sciences Society, Vol. 48, No. 5, 147, 17.07.2025.

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

Harvard

Gubarev, V & Panasenko, A 2025, 'Rota—Baxter operators on the simple Jordan algebra of matrices of order two', Bulletin of the Malaysian Mathematical Sciences Society, vol. 48, no. 5, 147. https://doi.org/10.1007/s40840-025-01932-3

APA

Gubarev, V., & Panasenko, A. (2025). Rota—Baxter operators on the simple Jordan algebra of matrices of order two. Bulletin of the Malaysian Mathematical Sciences Society, 48(5), [147]. https://doi.org/10.1007/s40840-025-01932-3

Vancouver

Gubarev V, Panasenko A. Rota—Baxter operators on the simple Jordan algebra of matrices of order two. Bulletin of the Malaysian Mathematical Sciences Society. 2025 Jul 17;48(5):147. doi: 10.1007/s40840-025-01932-3

Author

Gubarev, Vsevolod ; Panasenko, Alexander. / Rota—Baxter operators on the simple Jordan algebra of matrices of order two. In: Bulletin of the Malaysian Mathematical Sciences Society. 2025 ; Vol. 48, No. 5.

BibTeX

@article{da9fda86e3d542268609f41dc24760a5,
title = "Rota—Baxter operators on the simple Jordan algebra of matrices of order two",
abstract = "We describe all Rota—Baxter operators of any weight on the space of matrices from M2(F) considered under the product a∘b=(ab+ba)/2 and usually denoted as M2(F)(+). This algebra is known to be a simple Jordan one. We introduce symmetrized Rota—Baxter operators of weight λ and show that every Rota—Baxter operator of weight 0 on M2(F)(+) either is a Rota—Baxter operator of weight 0 on M2(F) or is a symmetrized Rota—Baxter operator of weight 0 on the same M2(F). We also prove that every Rota—Baxter operator of nonzero weight λ on M2(F)(+) is either a Rota—Baxter operator of weight λ on M2(F) or is, up to the action of ϕ:R→-R-λid, a symmetrized Rota—Baxter operator of weight λ on M2(F).",
keywords = "Jordan algebra, Rota—Baxter operator, matrix algebra",
author = "Vsevolod Gubarev and Alexander Panasenko",
note = "The authors are grateful to V.N. Zhelyabin and P.S. Kolesnikov for the helpful 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 = jul,
day = "17",
doi = "10.1007/s40840-025-01932-3",
language = "English",
volume = "48",
journal = "Bulletin of the Malaysian Mathematical Sciences Society",
issn = "0126-6705",
publisher = "Springer Singapore",
number = "5",

}

RIS

TY - JOUR

T1 - Rota—Baxter operators on the simple Jordan algebra of matrices of order two

AU - Gubarev, Vsevolod

AU - Panasenko, Alexander

N1 - The authors are grateful to V.N. Zhelyabin and P.S. Kolesnikov for the helpful 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 - 2025/7/17

Y1 - 2025/7/17

N2 - We describe all Rota—Baxter operators of any weight on the space of matrices from M2(F) considered under the product a∘b=(ab+ba)/2 and usually denoted as M2(F)(+). This algebra is known to be a simple Jordan one. We introduce symmetrized Rota—Baxter operators of weight λ and show that every Rota—Baxter operator of weight 0 on M2(F)(+) either is a Rota—Baxter operator of weight 0 on M2(F) or is a symmetrized Rota—Baxter operator of weight 0 on the same M2(F). We also prove that every Rota—Baxter operator of nonzero weight λ on M2(F)(+) is either a Rota—Baxter operator of weight λ on M2(F) or is, up to the action of ϕ:R→-R-λid, a symmetrized Rota—Baxter operator of weight λ on M2(F).

AB - We describe all Rota—Baxter operators of any weight on the space of matrices from M2(F) considered under the product a∘b=(ab+ba)/2 and usually denoted as M2(F)(+). This algebra is known to be a simple Jordan one. We introduce symmetrized Rota—Baxter operators of weight λ and show that every Rota—Baxter operator of weight 0 on M2(F)(+) either is a Rota—Baxter operator of weight 0 on M2(F) or is a symmetrized Rota—Baxter operator of weight 0 on the same M2(F). We also prove that every Rota—Baxter operator of nonzero weight λ on M2(F)(+) is either a Rota—Baxter operator of weight λ on M2(F) or is, up to the action of ϕ:R→-R-λid, a symmetrized Rota—Baxter operator of weight λ on M2(F).

KW - Jordan algebra

KW - Rota—Baxter operator

KW - matrix algebra

UR - https://www.mendeley.com/catalogue/21254f2a-64a7-306b-9b51-0e15607309ac/

UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=105011051466&origin=inward

U2 - 10.1007/s40840-025-01932-3

DO - 10.1007/s40840-025-01932-3

M3 - Article

VL - 48

JO - Bulletin of the Malaysian Mathematical Sciences Society

JF - Bulletin of the Malaysian Mathematical Sciences Society

SN - 0126-6705

IS - 5

M1 - 147

ER -

ID: 68585815