The deformations of symplectic structures by moment maps

We study deformations of symplectic structures on a smooth manifold $M$ via the quasi-Poisson theory. By a fact, we can deform a given symplectic structure $\omega$ to a new symplectic structure $\omega_t$ parametrized by some element $t$ in $\Lambda^2\mathfrak{g}$, where $\mathfrak{g}$ is the Lie algebra of a Lie group $G$. Moreover, we can get a lot of concrete examples for the deformations of symplectic structures on the complex projective space and the complex Grassmannian.