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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, 18.10.2024.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - Rota–Baxter Operators of Weight Zero on Upper-Triangular Matrices of Order Three
AU - Gubarev, Vsevolod
PY - 2024/10/18
Y1 - 2024/10/18
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.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