From Rota-Baxter operators to quasitriangular Lie bialgebra structures on $gl_2(\mathbb C)$

TL;DR

This paper classifies quasitriangular Lie bialgebra structures on $gl_2(\mathbb{C})$ by utilizing the classification of nonzero weight Rota-Baxter operators, linking algebraic operators to Lie bialgebra structures.

Contribution

It provides a novel classification of quasitriangular Lie bialgebras on $gl_2(\mathbb{C})$ through the analysis of Rota-Baxter operators of nonzero weight.

Findings

Complete classification of Rota-Baxter operators on $gl_2(\mathbb{C})$

Explicit description of quasitriangular Lie bialgebra structures

Connection established between Rota-Baxter operators and Lie bialgebras

Abstract

In the paper we describe structures of quasitriangular Lie bialgebra on $gl_2(\mathbb C)$ using the classification of Rota-Baxter operators of nonzero weight on $gl_2(\mathbb C)$.