Rota–Baxter operators of weight zero on the matrix algebra of order three without unit in kernel

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Rota–Baxter operators of weight zero on the matrix algebra of order three without unit in kernel. / Gubarev, Vsevolod.

In: Journal of Algebra, Vol. 683, 01.12.2025, p. 253-277.

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

BibTeX

@article{1ba7558c1e0b4bd2947d87cb2efe248f,

title = "Rota–Baxter operators of weight zero on the matrix algebra of order three without unit in kernel",

abstract = "We describe all Rota–Baxter operators R of weight zero on the matrix algebra M3(F) over a quadratically closed field F of characteristic not 2 or 3 such that R(1) ̸= 0. Thus, we get a partial classification of solutions to the associative Yang-Baxter equation on M3(F). For the solution, the computer algebra system Singular was involved.",

keywords = "Rota–Baxter operator, Matrix algebra",

author = "Vsevolod Gubarev",

note = "The research was carried out within the framework of the Sobolev Institute of Mathematics state contract (project FWNF-2022-0002).",

year = "2025",

month = dec,

day = "1",

doi = "10.1016/j.jalgebra.2025.06.019",

language = "English",

volume = "683",

pages = "253--277",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Elsevier Science Publishing Company, Inc.",

}

RIS

TY - JOUR

T1 - Rota–Baxter operators of weight zero on the matrix algebra of order three without unit in kernel

AU - Gubarev, Vsevolod

N1 - The research was carried out within the framework of the Sobolev Institute of Mathematics state contract (project FWNF-2022-0002).

PY - 2025/12/1

Y1 - 2025/12/1

N2 - We describe all Rota–Baxter operators R of weight zero on the matrix algebra M3(F) over a quadratically closed field F of characteristic not 2 or 3 such that R(1) ̸= 0. Thus, we get a partial classification of solutions to the associative Yang-Baxter equation on M3(F). For the solution, the computer algebra system Singular was involved.

AB - We describe all Rota–Baxter operators R of weight zero on the matrix algebra M3(F) over a quadratically closed field F of characteristic not 2 or 3 such that R(1) ̸= 0. Thus, we get a partial classification of solutions to the associative Yang-Baxter equation on M3(F). For the solution, the computer algebra system Singular was involved.

KW - Rota–Baxter operator

KW - Matrix algebra

UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=105009849077&origin=inward

U2 - 10.1016/j.jalgebra.2025.06.019

DO - 10.1016/j.jalgebra.2025.06.019

M3 - Article

VL - 683

SP - 253

EP - 277

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -

ID: 68404122