Matched pairs of Hopf algebras and Rota-Baxter Hopf algebras
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911294164041728 |
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| author | Wang, Shukun |
| author_facet | Wang, Shukun |
| contents | In this paper, we first study Rota-Baxter Hopf algebras of weight $-1$ and construct a matched pair of Hopf algebras on every Rota-Baxter Hopf algebra of weight $-1$. Then we propose the notion of projection homomorphism pairs on a matched pair of Hopf algebras, and show that every projection homomorphism pair $(C,\wtd{C})$ induces a Rota-Baxter Hopf algebra. Conversely, we prove that the matched pair of Hopf algebras on a Rota-Baxter Hopf algebra of weight $-1$ $(H,B)$ gives rise to a projection homomorphism pair $(C,\wtd{C})$. Furthermore, we study the Rota-Baxter Hopf algebra structure on $\im C$ that is Rota-Baxter isomorphic to $(H,B)$, and investigate the relationship between the Rota-Baxter Hopf algebra structure on $\im \wtd{C}$ and the descendent Rota-Baxter Hopf algebra $(H_{B},B)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_00286 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Matched pairs of Hopf algebras and Rota-Baxter Hopf algebras Wang, Shukun Rings and Algebras In this paper, we first study Rota-Baxter Hopf algebras of weight $-1$ and construct a matched pair of Hopf algebras on every Rota-Baxter Hopf algebra of weight $-1$. Then we propose the notion of projection homomorphism pairs on a matched pair of Hopf algebras, and show that every projection homomorphism pair $(C,\wtd{C})$ induces a Rota-Baxter Hopf algebra. Conversely, we prove that the matched pair of Hopf algebras on a Rota-Baxter Hopf algebra of weight $-1$ $(H,B)$ gives rise to a projection homomorphism pair $(C,\wtd{C})$. Furthermore, we study the Rota-Baxter Hopf algebra structure on $\im C$ that is Rota-Baxter isomorphic to $(H,B)$, and investigate the relationship between the Rota-Baxter Hopf algebra structure on $\im \wtd{C}$ and the descendent Rota-Baxter Hopf algebra $(H_{B},B)$. |
| title | Matched pairs of Hopf algebras and Rota-Baxter Hopf algebras |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2512.00286 |