3-Lie-Rinehart Algebras

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.

References in corpus (2)

• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Symplectic structures on $3$-Lie algebras

Cited by in corpus (4)

• On split regular Hom-Leibniz-Rinehart algebras
• Hom 3-Lie-Rinehart Algebras
• Extensions and crossed modules of $n$-Lie Rinehart algebras
• On 3-Hom-Lie-Rinehart algebras