The minimal model of Rota-Baxter operad with arbitrary weight
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866910535208927232 |
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| author | Wang, Kai Zhou, Guodong |
| author_facet | Wang, Kai Zhou, Guodong |
| contents | This paper investigates Rota-Baxter associative algebras of of arbitrary weights, that is, associative algebras endowed with Rota-Baxter operators of arbitrary weights from an operadic viewpoint. Denote by $\RB$ the operad of Rota-Baxter associative algebras. A homotopy cooperad is explicitly constructed, which can be seen as the Koszul dual of $\RB$ as it is proven that the cobar construction of this homotopy cooperad is exactly the minimal model of $\RB$. This enables us to give the notion of homotopy Rota-Baxter associative algebras. The deformation complex of a Rota-Baxter associative algebra and the underlying $L_\infty$-algebra structure over it are exhibited as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_02960 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The minimal model of Rota-Baxter operad with arbitrary weight Wang, Kai Zhou, Guodong K-Theory and Homology Rings and Algebras 18M70, 17B38, 16E40 This paper investigates Rota-Baxter associative algebras of of arbitrary weights, that is, associative algebras endowed with Rota-Baxter operators of arbitrary weights from an operadic viewpoint. Denote by $\RB$ the operad of Rota-Baxter associative algebras. A homotopy cooperad is explicitly constructed, which can be seen as the Koszul dual of $\RB$ as it is proven that the cobar construction of this homotopy cooperad is exactly the minimal model of $\RB$. This enables us to give the notion of homotopy Rota-Baxter associative algebras. The deformation complex of a Rota-Baxter associative algebra and the underlying $L_\infty$-algebra structure over it are exhibited as well. |
| title | The minimal model of Rota-Baxter operad with arbitrary weight |
| topic | K-Theory and Homology Rings and Algebras 18M70, 17B38, 16E40 |
| url | https://arxiv.org/abs/2203.02960 |