关键词: 3-李代数, 齐性Rota-Baxter 算子, 齐性Rota-Baxter 3-李代数

Abstract: Homogeneous Rota-Baxter operators R on the infinite dimensional simple 3-Lie Algebra A_ω=∑_m∈ZFL_m are Rota-Baxter operators which satisfy R(L_m)=f(m)L_m, where f:Z→Fis a function. Since Rota-Baxter operators of weight λ with λ≠0 on 3-Lie algebras are completely determined by the case λ=1, the homogeneous Rota-Baxter operators of weight 1 on A_ω with |W₁|<∞ are discussed. Five 3-Lie algebras(A,［,,］_j)are constructed by the simple 3-Lie algebra A_ω and its homogeneous Rota-Baxter operators.And it is proved that 3-Lie algebras(A,［,,］_j)are all homogeneous Rota-Baxter 3-Lie algebras.

Key words: 3-Lie algebra, homogeneous Rota-Baxter operator, homogeneous Rota-Baxter 3-Lie algebra