Homogeneous Rota-Baxter operators R 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→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 Aω with |W1|<∞ are discussed. Five 3-Lie algebras(A,［,,］j)are constructed by the simple 3-Lie algebra Aω and its homogeneous Rota-Baxter operators.And it is proved that 3-Lie algebras(A,［,,］j)are all homogeneous Rota-Baxter 3-Lie algebras.
BAI Ruipu
,
KANG Chuangchuang
,
MA Yue
,
HOU Shuai
,
BA Yi
. Homogeneous Rota-Baxter 3-Lie Algebras(Ⅰ)[J]. Journal of Hebei University(Natural Science Edition), 2018
, 38(1)
: 1
-6
.
DOI: 10.3969/j.issn.1000-1565.2018.01.001
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