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arxiv: math/0507468 · v1 · submitted 2005-07-22 · 🧮 math.QA · math-ph· math.MP

Quantum Spheres for OSp_q(1/2)

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keywords covariantnoncommutativequantumrealizationsupersphereadmitsalgebraalgebras
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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.

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