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Rota–Baxter Operators of Weight Zero on Upper-Triangular Matrices of Order Three. / Gubarev, Vsevolod.

в: Mediterranean Journal of Mathematics, Том 21, № 7, 200, 11.2024.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Gubarev, V 2024, 'Rota–Baxter Operators of Weight Zero on Upper-Triangular Matrices of Order Three', Mediterranean Journal of Mathematics, Том. 21, № 7, 200. https://doi.org/10.1007/s00009-024-02744-8

APA

Gubarev, V. (2024). Rota–Baxter Operators of Weight Zero on Upper-Triangular Matrices of Order Three. Mediterranean Journal of Mathematics, 21(7), [200]. https://doi.org/10.1007/s00009-024-02744-8

Vancouver

Gubarev V. Rota–Baxter Operators of Weight Zero on Upper-Triangular Matrices of Order Three. Mediterranean Journal of Mathematics. 2024 нояб.;21(7):200. doi: 10.1007/s00009-024-02744-8

Author

Gubarev, Vsevolod. / Rota–Baxter Operators of Weight Zero on Upper-Triangular Matrices of Order Three. в: Mediterranean Journal of Mathematics. 2024 ; Том 21, № 7.

BibTeX

@article{a05fc7295d794a7797ecffe93fbb50d2,
title = "Rota–Baxter Operators of Weight Zero on Upper-Triangular Matrices of Order Three",
abstract = "We describe all Rota–Baxter operators R of weight zero on the algebra U3(F) of upper-triangular matrices of order three over a field of characteristic 0. For this, we apply the following three ingredients: properties of R(1), conjugation with suitable (anti)automorphisms of U3(F), and computation with the help of Singular of the Gr{\"o}bner basis for the system of equations arisen on the coefficients of R.",
keywords = "16W99, Rota–Baxter operator, matrix algebra, upper-triangular matrix",
author = "Vsevolod Gubarev",
note = "The author is grateful to the anonymous reviewer for the helpful remarks. The study was supported by the Russian Science Foundation under Grant No. 23-71-10005, https://rscf.ru/project/23-71-10005/.",
year = "2024",
month = nov,
doi = "10.1007/s00009-024-02744-8",
language = "English",
volume = "21",
journal = "Mediterranean Journal of Mathematics",
issn = "1660-5446",
publisher = "Birkhauser Verlag Basel",
number = "7",

}

RIS

TY - JOUR

T1 - Rota–Baxter Operators of Weight Zero on Upper-Triangular Matrices of Order Three

AU - Gubarev, Vsevolod

N1 - The author is grateful to the anonymous reviewer for the helpful remarks. The study was supported by the Russian Science Foundation under Grant No. 23-71-10005, https://rscf.ru/project/23-71-10005/.

PY - 2024/11

Y1 - 2024/11

N2 - We describe all Rota–Baxter operators R of weight zero on the algebra U3(F) of upper-triangular matrices of order three over a field of characteristic 0. For this, we apply the following three ingredients: properties of R(1), conjugation with suitable (anti)automorphisms of U3(F), and computation with the help of Singular of the Gröbner basis for the system of equations arisen on the coefficients of R.

AB - We describe all Rota–Baxter operators R of weight zero on the algebra U3(F) of upper-triangular matrices of order three over a field of characteristic 0. For this, we apply the following three ingredients: properties of R(1), conjugation with suitable (anti)automorphisms of U3(F), and computation with the help of Singular of the Gröbner basis for the system of equations arisen on the coefficients of R.

KW - 16W99

KW - Rota–Baxter operator

KW - matrix algebra

KW - upper-triangular matrix

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85207240390&origin=inward&txGid=188cf3986479d203ad70d54bfcb57968

UR - https://elibrary.ru/item.asp?id=74779327

UR - https://www.mendeley.com/catalogue/c1807516-bbc0-340b-8150-f087574cc482/

U2 - 10.1007/s00009-024-02744-8

DO - 10.1007/s00009-024-02744-8

M3 - Article

VL - 21

JO - Mediterranean Journal of Mathematics

JF - Mediterranean Journal of Mathematics

SN - 1660-5446

IS - 7

M1 - 200

ER -

ID: 60779209