Formal integration of complete 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_ | 1866914320215965696 |
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| author | Goncharov, Maxim Kolesnikov, Pavel Sheng, Yunhe Tang, Rong |
| author_facet | Goncharov, Maxim Kolesnikov, Pavel Sheng, Yunhe Tang, Rong |
| contents | In this paper, first we revisit the formal integration of Lie algebras, which give rise to braces in some special cases. Then we establish the formal integration theory for complete Rota-Baxter Lie algebras, that is, we show that there is a Rota-Baxter group with the underlying group structure given by the Baker-Campbell-Hausdorff formula, associated to any complete Rota-Baxter Lie algebra. In particular, we use the post-Lie Magnus expansion to give the explicit formula of the Rota-Baxter operator. Finally we show that one can obtain a graded Rota-Baxter Lie ring from a filtered Rota-Baxter group. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_09261 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Formal integration of complete Rota-Baxter Lie algebras Goncharov, Maxim Kolesnikov, Pavel Sheng, Yunhe Tang, Rong Mathematical Physics Quantum Algebra Rings and Algebras In this paper, first we revisit the formal integration of Lie algebras, which give rise to braces in some special cases. Then we establish the formal integration theory for complete Rota-Baxter Lie algebras, that is, we show that there is a Rota-Baxter group with the underlying group structure given by the Baker-Campbell-Hausdorff formula, associated to any complete Rota-Baxter Lie algebra. In particular, we use the post-Lie Magnus expansion to give the explicit formula of the Rota-Baxter operator. Finally we show that one can obtain a graded Rota-Baxter Lie ring from a filtered Rota-Baxter group. |
| title | Formal integration of complete Rota-Baxter Lie algebras |
| topic | Mathematical Physics Quantum Algebra Rings and Algebras |
| url | https://arxiv.org/abs/2404.09261 |