An example of a simple double Lie algebra

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.

12 p.; v2 and v3: some definitions from Sec. 4 are corrected; Proposition 3 added, Sec. 5 is removed

References in corpus (2)

• Pre-Calabi-Yau algebras and double Poisson brackets
• Representations and Modules of Rota-Baxter Algebras