If ∆ and Γ are two derivations of a commutative algebra A such that ∆Γ-Γ∆ = ∆ is locally nilpotent, one can endow A with a new product * whose filtered semiclassical limit is the Poisson structure ∆ ∧ Γ. In this article we first study theses (Poisson) algebras from an algebraic point of view, and when A is a polynomial algebra, we investigate their homological properties. In particular, if the derivations ∆ and Γ are linear, we prove that the algebras (A, *) are Artin-Schelter regular algebras. Assuming furthermore a technical condition on Γ, we show that the algebra (A, *) is Calabi-Yau if and only if the trace of Γ is equal to 1 if and only if the Poisson algebra (A, ∆ ∧ Γ) is unimodular.