利用无限维单3-李代数Aω上权为1且满足g(0)+g(1)+1=0的齐性Rota-Baxter算子Rk,构造了13类齐性Rota-Baxter 3-李代数Ak,1≤k≤13,证明了在齐性Rota-Baxter 3-李代数Ak中存在5类两两不同构的齐性Rota-Baxter 3-李代数Di,并研究了每一类3-李代数Di的结构,1≤i≤5.
13 classes of homogeneous Rota-Baxter 3-Lie algebras Ak are constructed by using the homogeneous Rota-Baxter operators Rk, 1≤k≤13, with weight 1 and satisfying g(0)+g(1)+1=0 on infinite dimensional simple 3-Lie algebra Aω. It is proved that there are 5 classes of non-isomorphic homogeneous Rota-Baxter 3-Lie algebras Di,1≤i≤5, in the homogeneous Rota-Baxter 3-Lie Algebra Ak,1≤k≤13, and the structure of each class of 3-Lie algebras Di, 1≤i≤5, is studied.
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