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arXiv · 1903.12283

3-Lie-Rinehart Algebras

Ruipu Bai·Xiaojuan Li·Yingli Wu
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Abstract

In this paper, we define a class of 3-algebras which are called 3-Lie-Rinehart algebras. A 3-Lie-Rinehart algebra is a triple $(L, A, ρ)$, where $A$ is a commutative associative algebra, $L$ is an $A$-module, $(A, ρ)$ is a 3-Lie algebra $L$-module and $ρ(L, L)\subseteq Der(A)$. We discuss the basic structures, actions and crossed modules of 3-Lie-Rinehart algebras and construct 3-Lie-Rinehart algebras from given algebras, we also study the derivations from 3-Lie-Rinehart algebras to 3-Lie $A$-algebras. From the study, we see that there is much difference between 3-Lie algebras and 3-Lie-Rinehart algebras.

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Ruipu Bai, Xiaojuan Li, Yingli Wu. 2019-04-22. 3-Lie-Rinehart Algebras. https://arxiv.org/abs/1903.12283

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