Modified Rota-Baxter operators of non-zero weight on $3$-Lie algebras
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911353932873728 |
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| author | Guo, Shuangjian Qin, Yufei Zhou, Guodong |
| author_facet | Guo, Shuangjian Qin, Yufei Zhou, Guodong |
| contents | In this paper, we introduce the notion of modified Rota-Baxter operators of non-zero weight on $3$-Lie algebras and provide some examples. Next, we give various constructions of modified Rota-Baxter operators of non-zero weight according to constructions of $3$-Lie algebras. Furthermore, we define a cohomology of modified Rota-Baxter operators of non-zero weight on $3$-Lie algebras with coefficients in a suitable representation. As an application, we study formal deformations of modified Rota-Baxter operators of non-zero weight that are generated by the above-defined cohomology. In the final part of the paper, we construct two \(L_\infty[1]\)-algebra structures whose Maurer-Cartan elements correspond to relative and absolute modified Rota-Baxter \(3\)-Lie algebra structures of nonzero weight, respectively. Lastly, we compare our \(L_\infty[1]\)-algebraic approach with the deformation-controlling \(L_\infty[1]\)-algebra for relative Rota-Baxter \(3\)-Lie operators developed by Hou, Sheng, and Zhou. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_01942 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Modified Rota-Baxter operators of non-zero weight on $3$-Lie algebras Guo, Shuangjian Qin, Yufei Zhou, Guodong Rings and Algebras Representation Theory In this paper, we introduce the notion of modified Rota-Baxter operators of non-zero weight on $3$-Lie algebras and provide some examples. Next, we give various constructions of modified Rota-Baxter operators of non-zero weight according to constructions of $3$-Lie algebras. Furthermore, we define a cohomology of modified Rota-Baxter operators of non-zero weight on $3$-Lie algebras with coefficients in a suitable representation. As an application, we study formal deformations of modified Rota-Baxter operators of non-zero weight that are generated by the above-defined cohomology. In the final part of the paper, we construct two \(L_\infty[1]\)-algebra structures whose Maurer-Cartan elements correspond to relative and absolute modified Rota-Baxter \(3\)-Lie algebra structures of nonzero weight, respectively. Lastly, we compare our \(L_\infty[1]\)-algebraic approach with the deformation-controlling \(L_\infty[1]\)-algebra for relative Rota-Baxter \(3\)-Lie operators developed by Hou, Sheng, and Zhou. |
| title | Modified Rota-Baxter operators of non-zero weight on $3$-Lie algebras |
| topic | Rings and Algebras Representation Theory |
| url | https://arxiv.org/abs/2601.01942 |