利用无限维3-李代数Aω={Lm|m∈Z}上所有满足h(0)+h(1)+1≠0的齐性Rota-Baxter算子R, 构造了齐性Rota-Baxter 3-李代数, 其中h:Z→F,R(Lm)=h(m)Lm,∠m∈Z,并对所构造的3-李代数进行了分类, 证明了存在5类不同构的齐性Rota-Baxter 3-李代数Ck,1≤k≤5.
By homogenous Rota-Baxter operators R satisfying h(0)+h(1)+1≠0 on the infinite dimensional 3-Lie algebra Aω={Lm|m∈Z}, homogenous Rota-Baxter 3-Lie algebras are constructed and the classification is given, where h∶Z→F,R(Lm)=h(m)Lm,∠m∈Z. It is proved that there exist 5 classes homogenous Rota-Baxter 3-Lie algebras Ck,1≤k≤5.
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