3-李代数T的齐性Rota-Baxter算子

doi:10.6040/j.issn.1671-9352.0.2021.097

《山东大学学报(理学版)》 ›› 2021, Vol. 56 ›› Issue (8): 61-66.doi: 10.6040/j.issn.1671-9352.0.2021.097

• • 上一篇

3-李代数T的齐性Rota-Baxter算子

白瑞蒲^1,2,刘培^1,2

1.河北大学数学与信息科学学院, 河北保定 071002;2. 河北省机器学习与智能计算重点实验室, 河北保定 071002

发布日期:2021-08-09
作者简介:白瑞蒲(1960— ), 女, 博士, 教授, 研究方向为李群、李代数及多元李代数. E-mail:bairuipu@hbu.edu.cn
基金资助:
河北省自然科学基金资助项目(20182011126)

Homogeneous Rota-Baxter operators of 3-Lie algebra T

BAI Rui-pu^1,2, LIU Pei^1,2

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

摘要/Abstract

摘要： 主要研究实数域F上典型Nambu 3-李代数T=∑_{l∈z_≥1}Fy sin(lx)∑_{r∈z_≥0} Fz cos(rx)的权为1和权为0的齐性Rota-Baxter算子θ的结构, 其中θ满足存在两个整数集到F的可加映射α和β, 使得θ(y sin(lx))=α(l)y sin(lx), θ(z cos(rx))=β(r)z cos(rx)。证明了T上存在10种权为1的齐性Rota-Baxter算子, 存在4种权为0的齐性Rota-Baxter算子,并给出了每种算子的具体表达式。

关键词: 3-李代数, Rota-Baxter算子, 齐性Rota-Baxter算子

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

中图分类号:

O152.5

白瑞蒲,刘培. 3-李代数T的齐性Rota-Baxter算子[J]. 《山东大学学报(理学版)》, 2021, 56(8): 61-66.

BAI Rui-pu, LIU Pei. Homogeneous Rota-Baxter operators of 3-Lie algebra T[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(8): 61-66.

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3-李代数T的齐性Rota-Baxter算子

Homogeneous Rota-Baxter operators of 3-Lie algebra T

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