Associative Rota--Baxter operators on the Sweedler algebra $H_4$
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866918320963321856 |
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| author | Podkorytov, Maxim V. |
| author_facet | Podkorytov, Maxim V. |
| contents | In this paper, we classify all Rota--Baxter operators on the Sweedler algebra $H_4$ up to conjugation and dualization. Modulo algebra (anti)automorphisms of $H_4$, we first describe its subalgebras and then analyse the kernel of a Rota--Baxter operator. The classification is carried out according to the dimension of this kernel, yielding a complete description of such operators. A complete list of operators is given in the theorem of the final section. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_03133 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Associative Rota--Baxter operators on the Sweedler algebra $H_4$ Podkorytov, Maxim V. Rings and Algebras In this paper, we classify all Rota--Baxter operators on the Sweedler algebra $H_4$ up to conjugation and dualization. Modulo algebra (anti)automorphisms of $H_4$, we first describe its subalgebras and then analyse the kernel of a Rota--Baxter operator. The classification is carried out according to the dimension of this kernel, yielding a complete description of such operators. A complete list of operators is given in the theorem of the final section. |
| title | Associative Rota--Baxter operators on the Sweedler algebra $H_4$ |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2602.03133 |