Twisted Rota-Baxter family operators on Hom-associative algebras
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916456071954432 |
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| author | Teng, Wen Xiao, Yunpeng |
| author_facet | Teng, Wen Xiao, Yunpeng |
| contents | In this paper, we first define twisted Rota-Baxter family operators on Hom-associative algebras indexed by a semigroup $Ω$. Then we introduce and study Hom-NS-family algebras as the underlying structures of twisted Rota-Baxter family operators. Meanwhile, We show that a Hom-NS-family algebra induces an ordinary Hom-NS-algebra on the tensor product with the semigroup algebra. Moreover, we define the cohomology of a twisted Rota-Baxter family operator. This cohomology can also be viewed as the cohomology of a certain Hom-$Ω$-associative algebra with coefficients in a suitable bimodule. Finally, we examine deformations of twisted Rota-Baxter family operators and demonstrate that they are governed by the aforementioned cohomology. The concept of Nijenhuis elements linked to a twisted Rota-Baxter family operator is introduced to provide a sufficient condition for its rigidity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_20175 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Twisted Rota-Baxter family operators on Hom-associative algebras Teng, Wen Xiao, Yunpeng Rings and Algebras 16E40, 16S80, 16W99 In this paper, we first define twisted Rota-Baxter family operators on Hom-associative algebras indexed by a semigroup $Ω$. Then we introduce and study Hom-NS-family algebras as the underlying structures of twisted Rota-Baxter family operators. Meanwhile, We show that a Hom-NS-family algebra induces an ordinary Hom-NS-algebra on the tensor product with the semigroup algebra. Moreover, we define the cohomology of a twisted Rota-Baxter family operator. This cohomology can also be viewed as the cohomology of a certain Hom-$Ω$-associative algebra with coefficients in a suitable bimodule. Finally, we examine deformations of twisted Rota-Baxter family operators and demonstrate that they are governed by the aforementioned cohomology. The concept of Nijenhuis elements linked to a twisted Rota-Baxter family operator is introduced to provide a sufficient condition for its rigidity. |
| title | Twisted Rota-Baxter family operators on Hom-associative algebras |
| topic | Rings and Algebras 16E40, 16S80, 16W99 |
| url | https://arxiv.org/abs/2410.20175 |