Algebra, group, and Hopf Rota-Baxter operators
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915055984967680 |
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| author | Bardakov, Valeriy G. Nikonov, Igor M. Zhelaybin, Viktor N. |
| author_facet | Bardakov, Valeriy G. Nikonov, Igor M. Zhelaybin, Viktor N. |
| contents | We know definition of Rota--Baxter operators on different algebraic systems. For examples, on groups, on algebras, on Hopf algebras. On some algebraic systems it is possible to define different types of Rota--Baxter operators. For example, on group algebra it is possible to define Rota--Baxter operator as on associative algebra, group Rota--Baxter operator and Rota--Baxter operator as on a Hopf algebra. We are investigating the following question: What are connections between these operators? We are studying these questions for the Sweedler algebra $H_4$, that is 4-dimension non--cocommutative Hopf algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_07158 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Algebra, group, and Hopf Rota-Baxter operators Bardakov, Valeriy G. Nikonov, Igor M. Zhelaybin, Viktor N. Rings and Algebras Group Theory 16T05, 16S30, 16T25 We know definition of Rota--Baxter operators on different algebraic systems. For examples, on groups, on algebras, on Hopf algebras. On some algebraic systems it is possible to define different types of Rota--Baxter operators. For example, on group algebra it is possible to define Rota--Baxter operator as on associative algebra, group Rota--Baxter operator and Rota--Baxter operator as on a Hopf algebra. We are investigating the following question: What are connections between these operators? We are studying these questions for the Sweedler algebra $H_4$, that is 4-dimension non--cocommutative Hopf algebra. |
| title | Algebra, group, and Hopf Rota-Baxter operators |
| topic | Rings and Algebras Group Theory 16T05, 16S30, 16T25 |
| url | https://arxiv.org/abs/2412.07158 |