齐次Rota-Baxter 3-李代数(Ⅱ)

Homogeneous Rota-Baxter 3-Lie Algebras (Ⅱ)

无限维单3-李代数A_ω=sum from m∈Z FL_m上权为λ的齐次Rota-Baxter算子R是A_ω的Rota-Baxter算子,且满足R(L_m)=f(m) L_m,其中f:Z→F。当λ不等于零时,3-李代数的权为λ的Rota-Baxter算子完全由权为1的Rota-Baxter算子所决定。研究A_ω上满足f(0)=0,f(1)=-1,权为1且f在无穷多个偶数上取非零值的14类齐性Rota-Baxter算子的结构;在3-李代数A_ω的基底空间A上,利用齐次Rota-Baxter算子构造齐次Rota-Baxter 3-李代数(A,[,,]_j,R_j),1≤ j≤ 7,其中R_j是由f_j确定的齐次Rota-Baxter算子。

Homogeneous Rota-Baxter operators R with weight A on the infinite dimensional simple 3-Lie algebra Aω=∑m∈ZFLm are Rota-Baxter operators which satisfy R（Lm） = f（m）Lm , where f：Z → F is a function. Since Rota-Baxter operators of weight A with λ ≠ 0 on 3-Lie algebras are completely determined by the case λ= 1 . The structures of 14 homogeneous Rota-Baxter operators of weight 1 on Aω with f（0） = 0, f（ 1 ） = - 1 and f（m） ≠ 0 for the infinite even m are discussed. On the vector space A, homo- geneous Rota-Baxter 3-Lie algebras （A, [ ,, ], Ri） are constructed by the homogeneous Rota-Baxter operators, where Ri is the homogeneous Rota-Baxter operator determined by fj.