Deformation quantization of a hessian KV- structure on ${\mathbb{R}}^2$

This paper studies the quantization of the deformation of Hessian structures on a two-dimensional vector space, in the framework of Koszul-Vinberg algebras. We analyze how Hessian structures can be deformed to obtain quantum structures while preserving certain geometric and algebraic properties. The aim of the paper is to establish links between deformation theory and Hessian geometry.