Noncommutative Superspaces Covariant Under $OS{p}_q(1\mathrm{\mid }2)$ Algebra

Using the corepresentation of the quantum group $S{L}_q(2)$ a general method for constructing noncommutative spaces covariant under its coaction is developed. The method allows us to treat the quantum plane and Podle's’ quantum spheres in a unified way and to construct higher dimensional noncommutative spaces systematically. Furthermore, we extend the method to the quantum supergroup $OS{p}_q(1\mathrm{\mid }2)\mathrm{.}$ In particular, a one-parameter family of covariant algebras, which may be interpreted as noncommutative superspheres, is constructed.