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3-Lie-Rinehart Algebras

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arxiv 1903.12283 v2 pith:F2XBW3VV submitted 2019-03-28 math.RA math-phmath.MP

Ruipu Bai , Xiaojuan Li , Yingli Wu This is my paper · ORCID
classification math.RAmath-phmath.MP
keywords algebraslie-rinehartalgebramoduleactionsassociativebasiccalled
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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 $(L, A, \rho)$, where $A$ is a commutative associative algebra, $L$ is an $A$-module, $(A, \rho)$ is a 3-Lie algebra $L$-module and $\rho(L, L)\subseteq Der(A)$. 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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Cited by 1 Pith paper

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  1. Crossed modules of ternary Leibniz algebras

    math.RA 2025-01 reject novelty 4.0 of 10

    The paper transfers crossed modules from triassociative and Leibniz algebras to ternary Leibniz algebras, but omits the supporting computations and contains garbled formulas.

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