The Density Property for Generalized Calogero--Moser Spaces with Inner Degrees of Freedom

We prove the density property for generalized Calogero–Moser spaces with inner degrees of freedom. This allows us to describe the holomorphic automorphism group of these complex affine manifolds. These generalized Calogero–Moser spaces can also be understood as quiver varieties corresponding to moduli spaces of $\mathrm{S}\mathrm{U}(2)$ instantons on a non-commutative ${\mathbb{R}}^4$.