English

On the integration of relative Rota-Baxter Lie algebras

Rings and Algebras 2025-06-24 v1 Group Theory

Abstract

In this paper, we give the necessary and sufficient conditions of the integrability of relative Rota-Baxter Lie algebras via double Lie groups, matched pairs of Lie groups and factorization of diffeomorphisms respectively. We use the integrability of Rota-Baxter operators to characterize whether the Poisson-Lie group integrating a factorizable Lie bialgebra is again factorizable. We thoroughly study the integrability of Rota-Baxter operators on the unique nontrivial 2-dimensional Lie algebra. As a byproduct, we construct a matched pair of Lie algebras that can not be integrated to a matched pair of Lie groups.

Keywords

Cite

@article{arxiv.2410.23547,
  title  = {On the integration of relative Rota-Baxter Lie algebras},
  author = {Jun Jiang and Yunhe Sheng and Chenchang Zhu},
  journal= {arXiv preprint arXiv:2410.23547},
  year   = {2025}
}