Formal integration of complete Rota-Baxter Lie algebras and Magnus expansion Full article
| Journal |
Selecta Mathematica, New Series
ISSN: 1022-1824 , E-ISSN: 1420-9020 |
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| Output data | Year: 2026, Volume: 32, Number: 2, DOI: 10.1007/s00029-026-01128-y | ||||
| Tags | Rota-Baxter Lie algebra · Post-Lie algebra · Formal integration · Rota-Baxter group · Brace · Magnus expansion | ||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Министерство науки и высшего образования РФ | FWNF-2026-0017 |
Abstract:
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.
Cite:
Goncharov M.
, Kolesnikov P.
, Sheng Y.
, Tang R.
Formal integration of complete Rota-Baxter Lie algebras and Magnus expansion
Selecta Mathematica, New Series. 2026. V.32. N2. DOI: 10.1007/s00029-026-01128-y WOS Scopus OpenAlex
Formal integration of complete Rota-Baxter Lie algebras and Magnus expansion
Selecta Mathematica, New Series. 2026. V.32. N2. DOI: 10.1007/s00029-026-01128-y WOS Scopus OpenAlex
Dates:
| Submitted: | Oct 24, 2024 |
| Accepted: | Nov 22, 2025 |
| Published online: | Feb 10, 2026 |
Identifiers:
| Web of science: | WOS:001685887200001 |
| Scopus: | 2-s2.0-105029729548 |
| OpenAlex: | W4394867896 |
Citing:
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