Cohomology theory of Rota-Baxter family BiHom-$Ω$-associative algebras
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909266956255232 |
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| author | Liu, Jiaqi Song, Chao Zhang, Yuanyuan |
| author_facet | Liu, Jiaqi Song, Chao Zhang, Yuanyuan |
| contents | In this paper, we first introduce the concept of Rota-Baxter family BiHom-$Ω$-associative algebras, then we define the cochain complex of BiHom-$Ω$-associative algebras and verify it via Maurer-Cartan methods. Next, we further introduce and study the cohomology theory of Rota-Baxter family BiHom-$Ω$-associative algebras of weight $λ$ and show that this cohomology controls the corresponding deformations. Finally, we study abelian extensions of Rota-Baxter family BiHom-$Ω$-associative algebras in terms of the second cohomology group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_17323 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cohomology theory of Rota-Baxter family BiHom-$Ω$-associative algebras Liu, Jiaqi Song, Chao Zhang, Yuanyuan Rings and Algebras 16W99 In this paper, we first introduce the concept of Rota-Baxter family BiHom-$Ω$-associative algebras, then we define the cochain complex of BiHom-$Ω$-associative algebras and verify it via Maurer-Cartan methods. Next, we further introduce and study the cohomology theory of Rota-Baxter family BiHom-$Ω$-associative algebras of weight $λ$ and show that this cohomology controls the corresponding deformations. Finally, we study abelian extensions of Rota-Baxter family BiHom-$Ω$-associative algebras in terms of the second cohomology group. |
| title | Cohomology theory of Rota-Baxter family BiHom-$Ω$-associative algebras |
| topic | Rings and Algebras 16W99 |
| url | https://arxiv.org/abs/2407.17323 |