On the integration of relative Rota-Baxter Lie algebras
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911017456369664 |
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| author | Jiang, Jun Sheng, Yunhe Zhu, Chenchang |
| author_facet | Jiang, Jun Sheng, Yunhe Zhu, Chenchang |
| contents | In this paper, we give the necessary and sufficient conditions of the integrability of relative Rota-Baxter Lie algebras via double Lie groups, matched pairs of Lie groups and factorization of diffeomorphisms respectively. We use the integrability of Rota-Baxter operators to characterize whether the Poisson-Lie group integrating a factorizable Lie bialgebra is again factorizable. We thoroughly study the integrability of Rota-Baxter operators on the unique nontrivial 2-dimensional Lie algebra. As a byproduct, we construct a matched pair of Lie algebras that can not be integrated to a matched pair of Lie groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_23547 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the integration of relative Rota-Baxter Lie algebras Jiang, Jun Sheng, Yunhe Zhu, Chenchang Rings and Algebras Group Theory 22E60, 17B38 In this paper, we give the necessary and sufficient conditions of the integrability of relative Rota-Baxter Lie algebras via double Lie groups, matched pairs of Lie groups and factorization of diffeomorphisms respectively. We use the integrability of Rota-Baxter operators to characterize whether the Poisson-Lie group integrating a factorizable Lie bialgebra is again factorizable. We thoroughly study the integrability of Rota-Baxter operators on the unique nontrivial 2-dimensional Lie algebra. As a byproduct, we construct a matched pair of Lie algebras that can not be integrated to a matched pair of Lie groups. |
| title | On the integration of relative Rota-Baxter Lie algebras |
| topic | Rings and Algebras Group Theory 22E60, 17B38 |
| url | https://arxiv.org/abs/2410.23547 |