Lie-Rinehart algebra of a r-Jacobi algebra

Abstract

We denote by A a commutative and unitary algebra over a commutative field K of characteristic zero and an integer r greater than or equal to 1. In studying the concept of r-Jacobi algebra on A; we construct an ordinary Lie algebra from which we deduce a structure of Lie-Rinehart algebra. We define the 1-canonical form of a r-Jacobi algebra.