Some constructions of 3-pre-Lie-Rinehart algebras

被引：1

作者：

Ben Hassine, Abdelkader ^{[1
,2
]}

Chtioui, Taoufik ^{[3
]}

Nasser, Nawel ^{[2
]}

机构：

[1] Univ Bisha, Coll Sci, Dept Math, Bisha, Saudi Arabia

[2] Univ Sfax, Fac Sci, Sfax, Tunisia

[3] Univ Gabes, Fac Sci Gabes, Gabes 6072, Tunisia

来源：

COMMUNICATIONS IN ALGEBRA | 2025年 / 53卷 / 04期

关键词：

3-Lie-Rinehart algebra; 3-pre-Lie-Rinehart algebra; Lie-Rinehart algebra; relative Rota-Baxter operator; representation; trace function; LIE-RINEHART ALGEBRA; BAXTER ALGEBRAS;

D O I：

10.1080/00927872.2024.2413699

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

3-Lie-Rinehart algebras are an algebraic axiomatization of the basic properties of Filippov algebroids (for n = 3). The purpose of this paper is to introduce the notion of relative Rota-Baxter operators on a 3-Lie-Rinehart algebra and give some classical characterizations. Next, we define 3-pre-Lie-Rinehart algebras which can be seen as a dendrification of 3-Lie-Rinehart algebras by means of relative Rota-Baxter operators. Moreover, we introduce the notion of trace functions on Lie-Rinehart algebra and pre-Lie-Rinehart algebra to construct their induced 3-Lie-Rinehart algebra and 3-pre-Lie-Rinehart algebra, respectively.

引用

页码：1470 / 1487

页数：18

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