Rota-Baxter operators of weight zero on the matrix algebra of order three without unit in kernel
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912542561927168 |
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| author | Gubarev, Vsevolod |
| author_facet | Gubarev, Vsevolod |
| contents | We describe all Rota-Baxter operators $R$ of weight zero on the matrix algebra $M_3(F)$ over a quadratically closed field $F$ of characteristic not 2 or 3 such that $R(1)\neq0$. Thus, we get a partial classification of solutions to the associative Yang-Baxter equation on $M_3(F)$. For the solution, the computer algebra system Singular was involved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_00825 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rota-Baxter operators of weight zero on the matrix algebra of order three without unit in kernel Gubarev, Vsevolod Rings and Algebras 16W99 We describe all Rota-Baxter operators $R$ of weight zero on the matrix algebra $M_3(F)$ over a quadratically closed field $F$ of characteristic not 2 or 3 such that $R(1)\neq0$. Thus, we get a partial classification of solutions to the associative Yang-Baxter equation on $M_3(F)$. For the solution, the computer algebra system Singular was involved. |
| title | Rota-Baxter operators of weight zero on the matrix algebra of order three without unit in kernel |
| topic | Rings and Algebras 16W99 |
| url | https://arxiv.org/abs/2412.00825 |