On the integration of relative Rota-Baxter Lie algebras
arXiv:2410.23547 · doi:10.1007/s00031-025-09920-4
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.
References in corpus (9)
- Renormalization in quantum field theory and the Riemann-Hilbert problem I: the Hopf algebra structure of graphs and the main theorem
- What a classical r-matrix really is
- Nonabelian generalized Lax pairs, the classical Yang-Baxter equation and PostLie algebras
- A Unified Algebraic Approach to Classical Yang-Baxter Equation
- Integration and geometrization of Rota-Baxter Lie algebras
- From double Lie groupoids to local Lie 2-groupoids
- Rota-Baxter operators on groups
- Factorizable Lie bialgebras, quadratic Rota-Baxter Lie algebras and Rota-Baxter Lie bialgebras
- Rota--Baxter operators and skew left brace structures over Heisenberg Group