We establish that Poisson cohomology is precisely the cohomology of the Lie algebra over  with coefficients in the adjoint representation of its Poisson module structure.

Poisson algebra, Poisson form, Lie-Rinehart algebra, differential algebra, modules of differential.

Received: October 27, 2023;  Accepted: December 22, 2023; Published: February 5, 2024

How to cite this article: S. C. Gatse, A. M. Mavambou and O. M. Mikanou, Lie-Rinehart algebras on Kaehler differential and Poisson algebras cohomology, JP Journal of Algebra, Number Theory and Applications 63(2) (2024), 111-129. http://dx.doi.org/10.17654/0972555524007

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