Kv-Cohomology of Koszul–vinberg Algebroids and Poisson Manifolds

The main concern of this paper is the study of the relationships between the KV-cohomology of Koszul–Vinberg algebras and some properties of various geometrical objects. In particular we show how the scalar KV-cohomology of real or holomorphic Koszul–Vinberg algebroids is closely related to real or holomorphic Poisson manifolds. In the appendix we point out strong relationships between the pioneer work of Nijenhuis [42] and the KV-cohomology.