JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (8): 61-66.doi: 10.6040/j.issn.1671-9352.0.2021.097

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Homogeneous Rota-Baxter operators of 3-Lie algebra T

BAI Rui-pu1,2, LIU Pei1,2   

  1. 1. College of Mathematics and Information Science, Hebei University, Baoding 071002, Hebei, China;
    2. Key Laboratory of Machine Learning and Computational Intelligence of Hebei Province, Baoding 071002, Hebei, China
  • Published:2021-08-09

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Abstract: Structure of homogeneous Rota-Baxter operators θ on the classical Nambu 3-Lie algebra T=∑l∈z≥1 Fy sin(lx)∑r∈z≥0Fz cos(rx)over the real field F of weight 1 and weight 0 is studied, where θ satisfies that there are two additive mappings α, β from the integers to F such that θ(y sin(lx))=α(l)y sin(lx), θ(z cos(rx))=β(r)z cos(rx). It is proved that there exist 10 non-zero homogeneous Rota-Baxter operators of weight 1, and 4 non-zero homogeneous Rota-Baxter operators of weight 0, and concrete expression of them are given.

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

CLC Number: 

  • O152.5
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