Differential Calculus on Quantum Spheres

1998/02/18 by Martin Welk, Welk, Martin · 2 citations
Mathematics · #17B37 #46L87 #81R50 #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #msc:17B37 #msc:46L87 #msc:81R50

paper · pdf · doi:10.48550/arxiv.math/9802087

27 pages, no figures, Latex2e. The classification of first order differential calculi which was collapsed by an error in the first version of this paper has been corrected and, at the same time, extended to a more general situation

arxiv created 1998/05/03 · arxiv updated 2009/11/30

Abstract

We study covariant differential calculus on the quantum spheres S_q²N-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.

Cited by

• Torsion-Free Bimodule Connections and the Maximal Prolongation of a First-Order Differential Calculus
• Takeuchi-Schneider equivalence and calculi for homogeneous spaces of Hopf algebroids

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