Noncommutative Superspaces Covariant Under $OS{p}_q(1|2)$ Algebra

Abstract

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 Podleś' quantum spheres in a unified way and to construct higher dimensional noncommutative spaces systematically. Furthermore, we extend the method to the quantum supergroup $OS{p}_q(1|2).$ In particular, a one-parameter family of covariant algebras, which may be interpreted as noncommutative superspheres, is constructed.

12pages, no figure, Submitted for the Proceedings of "IV. International Symposium, Quantum Theory and Symmetries", Varna, 2005