On quasi-Poisson Cohomology

Let $A$ be a Poisson algebra and $\text{Q}(A)$ its quasi-Poisson enveloping algebra. In this paper, the Yoneda-Ext algebra ${\text{Ext}}_{\text{Q}(A)}^{\ast }(A,A)$, which we call the quasi-Poisson cohomology algebra of $A$, is investigated. We construct a projective resolution of $A$ as $\text{Q}(A)$-modules, which enables to compute the quasi-Poisson cohomologies in a standard way. To simplify calculation, we also introduce the quasi-Poisson complex and apply to obtain quasi-Poisson cohomologies in some special cases.