Projective quantum spaces

Abstract

Associated to the standard $S{U}_q(n)$ R-matrices, we introduce quantum spheres $S_q^{2n-1}$, projective quantum spaces $C{P}_q^{n-1}$, and quantum Grassmann manifolds $G_k(C_q^n)$. These algebras are shown to be homogeneous quantum spaces of standard quantum groups and are also quantum principle bundles in the sense of T Brzezinski and S. Majid (Comm. Math. Phys. 157,591 (1993)).

8 pages