An example of a simple double Lie algebra

TL;DR

This paper extends the theory of double Lie algebras to infinite-dimensional cases and provides the first example of a simple double Lie algebra, advancing understanding in algebraic structures.

Contribution

It introduces the first example of a simple double Lie algebra and extends the correspondence to infinite-dimensional matrix algebras.

Findings

Established a correspondence between double Lie algebras and Rota-Baxter operators in infinite dimensions

Provided the first example of a simple double Lie algebra

Extended theoretical framework to infinite-dimensional cases

Abstract

We extend the correspondence between double Lie algebras and skew-symmetric Rota-Baxter operators of weight 0 on the matrix algebra for the infinite-dimensional case. We give the first example of a simple double Lie algebra.