Differential Calculus on Quantum Spheres
Martin Welk
TL;DR
This paper develops a framework for covariant differential calculus on quantum spheres, classifying first order calculi and establishing foundational structures for noncommutative geometry.
Contribution
It provides the first classification results for covariant first order differential calculi on quantum spheres and introduces a comprehensive framework including higher order calculi.
Findings
Two classification results for covariant first order differential calculi
A framework for higher order calculi and symmetry concepts
A specific first order calculus obtained by factorization
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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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Operator Algebra Research · Advanced Topics in Algebra