Rota-Baxter operators of weight zero on upper-triangular matrices of order three
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866918126848835584 |
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| author | Gubarev, Vsevolod |
| author_facet | Gubarev, Vsevolod |
| contents | We describe all Rota-Baxter operators $R$ of weight zero on the algebra $U_3(F)$ 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 $U_3(F)$, and computation with the help of \texttt{Singular} of the Gröbner basis for the system of the equations arisen on the coefficients of $R$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_00289 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rota-Baxter operators of weight zero on upper-triangular matrices of order three Gubarev, Vsevolod Rings and Algebras We describe all Rota-Baxter operators $R$ of weight zero on the algebra $U_3(F)$ 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 $U_3(F)$, and computation with the help of \texttt{Singular} of the Gröbner basis for the system of the equations arisen on the coefficients of $R$. |
| title | Rota-Baxter operators of weight zero on upper-triangular matrices of order three |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2404.00289 |