Rota Baxter operators of the simple 3-Lie algebra I

BAI Ruipu, CHENG Rong and ZHAN

Abstract

This paper studies Rota-Baxter operators on the simple 3-Lie algebras over the complex field. It is proved that there does not exist Rota-Baxter operators of weight zero with rank 3 on the simple 3-Lie algebras. And it provides the Rote-Baxter operators of weight zero with rank 1, 2, 4, respectively .