华东师范大学学报（自然科学版） >

2021 , Vol. 2021 >Issue 6: 15 - 23

DOI: https://doi.org/10.3969/j.issn.1000-5641.2021.06.002

数学

3-李-Rinehart代数的结构

  • 白瑞蒲 ,
  • 李晓娟
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  • 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
白瑞蒲，女，博士, 教授，研究方向为李群李代数、多元李代数. E-mail: bairuipu@hbu.edu.cn

收稿日期: 2020-04-01

  网络出版日期: 2021-11-26

基金资助

河北省自然科学基金(20182011126)

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The structure of 3-Lie-Rinehart algebras

  • Ruipu BAI ,
  • Xiaojuan LI
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  • 1. College of Mathematics and Information Science, Hebei University, Baoding Hebei 　071002, China
    2. Key Laboratory of Machine Learning and Computational Intelligence of Hebei Province, Baoding Hebei　　071002, China

Received date: 2020-04-01

  Online published: 2021-11-26

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摘要

定义了一类新的3元代数结构—3-李-Rinehart代数, 并对3-李-Rinehart代数的基本结构进行了研究. 用3元任意次可微函数、已知的3-李代数的模及3-李代数的内导子李代数分别构造了3-李-Rinehart代数及李-Rinehart代数.

关键词： 3-李代数; 交换结合代数; 3-李-Rinehart代数

本文引用格式

白瑞蒲 , 李晓娟 . 3-李-Rinehart代数的结构[J]. 华东师范大学学报（自然科学版）, 2021 , 2021(6) : 15 -23 . DOI: 10.3969/j.issn.1000-5641.2021.06.002

Abstract

In this paper, we introduce a class of 3-ary algebras, called the 3-Lie-Rinehart algebra, and we discuss the basic structure thereof. The 3-Lie-Rinehart algebras are constructed using 3-ary differentiable functions, modules of known 3-Lie algebras, and inner derivatives of 3-Lie algebras.

Key words： 3-Lie algebra; commutative associative algebra; 3-Lie-Rinehart algebra

参考文献

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