1998•arXiv (Cornell University)Open access

Differential Calculus on Quantum Spheres

Martin Welk

Abstract

We study covariant differential calculus on the quantum spheres S_q^2N-1. Two classification results for covariant first order differential calculi are proved. As an important step towards a description of the noncommutative geometry of the quantum spheres, a framework of covariant differential calculus is established, including a particular first order calculus obtained by factorization, higher order calculi and a symmetry concept.

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Key concepts: Differential calculus, Covariant transformation, Quantum differential calculus, Noncommutative geometry, Time-scale calculus, Calculus (dental), Mathematics, Differential (mechanical device)