In noncommutative algebraic geometry a commonly studied family of objects are  quantum projective spaces. Theses are certain deformations of the homogeneous coordinate ring of $\mathbb{CP}^n$. For example, see this [mathoverflow post][1]. The obvious question I would like to ask is whether or not people consider a Grassmannian generalisation of such objects, and if so, what are some well-known references.


  [1]: http://mathoverflow.net/questions/109347/point-modules-of-quantum-projective-space-mathbbpn