JACOBI STRUCTURES ON A LIE-RINEHART ALGEBRA
We define the Schouten-Nijenhuis bracket on the algebra of module of Kähler differentials and provide the main features of Jacobi manifolds by using the universal property of first order differential operators. Further, we establish the equivalence between a Lie-Rinehart algebra structure and a Jacobi structure and recover Lichnerowicz’s notion of Jacobi pair on a smooth manifold.
first order differential operator, Jacobi manifold, Schouten-Nijenhuis bracket, Lie-Rinehart algebra.
Received: May 2, 2022; Accepted: June 21, 2022; Published: September 30, 2022
How to cite this article: N. Mahoungou Moukala, M. M. Milounguidi and B. G. R. Bossoto, Jacobi structures on a Lie-Rinehart algebra, JP Journal of Geometry and Topology 28 (2022), 55-79. http://dx.doi.org/10.17654/0972415X22009
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