Journal of East China Normal University(Natural Science) >

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

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

Mathematics

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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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

Cite this article

Ruipu BAI , Xiaojuan LI . The structure of 3-Lie-Rinehart algebras[J]. Journal of East China Normal University(Natural Science), 2021 , 2021(6) : 15 -23 . DOI: 10.3969/j.issn.1000-5641.2021.06.002

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