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Formal integration of complete Rota-Baxter Lie algebras · arXivDesk

2404.09261Apr 14, 202423 pages. Compare to the previous version: 1. we give the formal integration formula using Magnus expansion, which is very surprised (the second half of Section 4); 2. we show that conversely one can obtain a Rota-Baxter Lie ring from a filtered Rota-Baxter group (Section 5)

Formal integration of complete Rota-Baxter Lie algebras

Maxim Goncharov, Pavel Kolesnikov, Yunhe Sheng, Rong Tang

Mathematical Physics Quantum Algebra Rings and Algebras

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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.

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The paper addresses: Formal integration of complete Rota-Baxter Lie algebras.
In this paper, first we revisit the formal integration of Lie algebras, which give rise to braces in some special cases.

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Author comment: 23 pages. Compare to the previous version: 1. we give the formal integration formula using Magnus expansion, which is very surprised (the second half of Section 4); 2. we show that conversely one can obtain a Rota-Baxter Lie ring from a filtered Rota-Baxter group (Section 5)