Noncommutative Superspaces Covariant Under $OSp_q(1|2)$ Algebra

Details Noncommutative Superspaces Covariant Under $OSp_q(1|2)$ Algebra Noncommutative Superspaces Covariant Under $OSp_q(1|2)$ Algebra

2005-11-17

arxiv.org/abs/math/0511436v1

Mathematics

Quantum Algebra

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

Scientific paper

Using the corepresentation of the quantum group $ SL_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 $ OSp_q(1|2).$ In particular, a one-parameter family of covariant algebras, which may be interpreted as noncommutative superspheres, is constructed.

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