Quantum Spheres for OSp_q(1/2)

Abstract

Using the corepresentation of the quantum supergroup OSp_q(1/2) a general method for constructing noncommutative spaces covariant under its coaction is developed. In particular, a one-parameter family of covariant algebras, which may be interpreted as noncommutative superspheres, is constructed. It is observed that embedding of the supersphere in the OSp_q(1/2) algebra is possible. This realization admits infinitesimal characterization a la Koornwinder. A covariant oscillator realization of the supersphere is also presented.

30pages, no figure. to be published in J. Math. Phys

References in corpus (6)

• Quantum Field Theory on Noncommutative Spaces
• Differential Calculus on the Quantum Superspace and Deformation of Phase Space
• Integrable quantum field theories with OSP(m/2n) symmetries
• Integrable quantum field theories with supergroup symmetries: the $OSP(1/2)$ case
• Noncommutative Geometry of Super-Jordanian $OS{p}_h(2/1)$ Covariant Quantum Space
• Jordanian quantum spheres

Cited by in corpus (6)

• Basic Hypergeometric Functions and Covariant Spaces for Even Dimensional Representations of U_q[osp(1/2)]
• Covariant Differential Calculi on $S{P}_q^{1|2}$
• Coherent State on SUq(2) Homogeneous Space
• Universal T-matrix, Representations of OSp_q(1/2) and Little Q-Jacobi Polynomials
• On super-Jordanian ${\mathcal{U}}_{\mathsf{h}}(sl(N|1))$ algebra
• Hopf algebra structure on symplectic superspace ${\mathrm{SP}}_q^{2|1}$