Abstract
AbstractIn this paper, we establish a local Lie theory for relative Rota–Baxter operators of weight 1. First we recall the category of relative Rota–Baxter operators of weight 1 on Lie algebras and construct a cohomology theory for them. We use the second cohomology group to study infinitesimal deformations of relative Rota–Baxter operators and modified ‐matrices. Then we introduce a cohomology theory of relative Rota–Baxter operators on a Lie group. We construct the differentiation functor from the category of relative Rota–Baxter operators on Lie groups to that on Lie algebras, and extend it to the cohomology level by proving the Van Est theorem between the two cohomology theories. We integrate a relative Rota–Baxter operator of weight 1 on a Lie algebra to a local relative Rota–Baxter operator on the corresponding Lie group, and show that the local integration and differentiation are adjoint to each other. Finally, we give two applications of our integration of Rota–Baxter operators: one is to give an explicit formula for the factorization problem, and the other is to provide an integration for matched pairs.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.