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.