Monomial Rota-Baxter operators of weight zero and averaging operators on the polynomial algebra
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913624958697472 |
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| author | Khodzitskii, Artem |
| author_facet | Khodzitskii, Artem |
| contents | Starting with the work S.H. Zheng, L. Guo and M. Rosenkranz (2015), Rota-Baxter operators are studied on the polynomial algebra. Injective Rota-Baxter operators of weight zero on $F[x]$ were described in 2021. We classify the following classes of monomial Rota-Baxter operators of weight zero on the polynomial algebra $F[x,y]$ and its augmentation ideal $F_0[x,y]$: 1) non-increasing in degree that do not contain monomials in the kernel, 2) mapping all monomials to themselves with a coefficient. In the context of these sets of operators, we show how one may define a monomial averaging operator by a given RB-operator and vice versa. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_18236 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Monomial Rota-Baxter operators of weight zero and averaging operators on the polynomial algebra Khodzitskii, Artem Rings and Algebras Starting with the work S.H. Zheng, L. Guo and M. Rosenkranz (2015), Rota-Baxter operators are studied on the polynomial algebra. Injective Rota-Baxter operators of weight zero on $F[x]$ were described in 2021. We classify the following classes of monomial Rota-Baxter operators of weight zero on the polynomial algebra $F[x,y]$ and its augmentation ideal $F_0[x,y]$: 1) non-increasing in degree that do not contain monomials in the kernel, 2) mapping all monomials to themselves with a coefficient. In the context of these sets of operators, we show how one may define a monomial averaging operator by a given RB-operator and vice versa. |
| title | Monomial Rota-Baxter operators of weight zero and averaging operators on the polynomial algebra |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2412.18236 |