Formal integration of complete Rota-Baxter Lie algebras

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.