Rota–Baxter Operators on Compact Simple Lie Groups and Algebras
Abstract
A smooth mapping $$ B \colon G \to G $$ on a Lie group $$ G $$ is called a Rota–Baxter operator if $$ B(g)B(h)=B(gB(g)hB(g)^{-1}) $$ for all $$ g, h \in G$$ . This concept was introduced in 2021 by Guo, Lang, and Sheng as a group analog of weight 1 Rota–Baxter operators on Lie algebras. In this paper, we prove that, on compact simple Lie groups, the only possible Rota–Baxter operators are the trivial mapping and the inversion. A similar description is given for weight 1 Rota–Baxter operators on compact simple Lie algebras.
Fields of Study & Subjects
Advanced Topics in Algebra
Matrix Theory and Algorithms
Holomorphic and Operator Theory
Publication details
- Journal / source
- Mathematical Notes
- Publisher
- Pleiades Publishing Ltd
- Volume
- 120
- Issue
- 3-4
- Pages
- 731–735
- Publication date
- 23 September 2026
- Language
- EN