Formal integration of complete Rota-Baxter Lie algebras and Magnus expansion

• Maxim Goncharov ^[1] ; Pavel Kolesnikov ^[1] ; Yunhe Sheng ^[2] ; Rong Tang ^[2]
  1. [1] Sobolev Institute of Mathematics

     Sobolev Institute of Mathematics

     Rusia

     
  2. [2] Jilin University

     Jilin University

     China

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 32, Nº. 2, 2026
• Idioma: inglés
• DOI: 10.1007/s00029-026-01128-y
• Enlaces
  • Texto completo
• Resumen

  • 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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