Deformation theory and Koszul duality for Rota-Baxter systems
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| Format: | Preprint |
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2025
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| _version_ | 1866913715329171456 |
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| author | Qin, Yufei Wang, Kai Zhou, Guodong |
| author_facet | Qin, Yufei Wang, Kai Zhou, Guodong |
| contents | This paper investigates Rota-Baxter systems in the sense of Brzeziński from the perspective of operad theory. The minimal model of the Rota-Baxter system operad is constructed, equivalently a concrete construction of its Koszul dual homotopy cooperad is given. The concept of homotopy Rota-Baxter systems and the $L_\infty$-algebra that governs deformations of a Rota-Baxter system are derived from the Koszul dual homotopy cooperad. The notion of infinity-Yang-Baxter pairs is introduced, which is a higher-order generalization of the traditional Yang-Baxter pairs. It is shown that a homotopy Rota-Baxter system structure on the endomorphism algebra of a graded space is equivalent to an associative infinity-Yang-Baxter pair on this graded algebra, thereby generalizing the classical correspondence between Yang-Baxter pairs and Rota-Baxter systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_01316 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Deformation theory and Koszul duality for Rota-Baxter systems Qin, Yufei Wang, Kai Zhou, Guodong Rings and Algebras Representation Theory 16E40 16S80 17B38 18M65 18M70 This paper investigates Rota-Baxter systems in the sense of Brzeziński from the perspective of operad theory. The minimal model of the Rota-Baxter system operad is constructed, equivalently a concrete construction of its Koszul dual homotopy cooperad is given. The concept of homotopy Rota-Baxter systems and the $L_\infty$-algebra that governs deformations of a Rota-Baxter system are derived from the Koszul dual homotopy cooperad. The notion of infinity-Yang-Baxter pairs is introduced, which is a higher-order generalization of the traditional Yang-Baxter pairs. It is shown that a homotopy Rota-Baxter system structure on the endomorphism algebra of a graded space is equivalent to an associative infinity-Yang-Baxter pair on this graded algebra, thereby generalizing the classical correspondence between Yang-Baxter pairs and Rota-Baxter systems. |
| title | Deformation theory and Koszul duality for Rota-Baxter systems |
| topic | Rings and Algebras Representation Theory 16E40 16S80 17B38 18M65 18M70 |
| url | https://arxiv.org/abs/2503.01316 |