On Grassmannians over *-rings Original Research Article

By [M. Golasi image ski, F. Gómez Ruiz, Polynomial and regular maps into Grassmannians, submitted] the tangent bundle TGn,r(K) of the Grassmannian Gn,r(K) is diffeomorphic to the manifold Idemn,r(K) of idempotent n×n matrices with rank r for K the reals, complex numbers or quaternions. Furthermore, a regular deformation retraction of affine varieties image Γn,r(K):Idemn,r(K)→Gn,r(K)can be described explicitly. Given a ring R with involution a notion of a Grassmannian and its normal and tangent bundle over R is studied. Then the above results are raised in that context provided appropriate properties for the ring R. In particular, this holds for any C*-algebra and a localization of some coordinate rings.