Algebraic K₀ of the Quantum Sphere and Noncommutative Index Theorem

1998/09/16 by Piotr M. Hajac, Hajac, Piotr M.
Mathematics · #FOS: Mathematics #K-Theory and Homology (math.KT) #Quantum Algebra (math.QA) #math.KT #math.QA

paper · pdf · doi:10.48550/arxiv.math/9809086

AMS-LaTeX, 8 pages

arxiv created 1998/09/16 · arxiv updated 2009/11/30

Abstract

The Noncommutative Index Theorem is used to prove that the Chern character of quantum Hopf line bundles over the standard Podles quantum sphere equals the winding number of the representations defining these bundles. This result gives an estimate of the positive cone of the algebraic K₀ of the standard quantum sphere.

Related

• Noncommutative index theory for mirror quantum spheres
• On the noncommutative spin geometry of the standard Podles sphere and index computations
• The Quantum Flag Manifold \mathbfSU_q(3)/\mathbbT² as an Example of a Noncommutative Sphere Bundle
• Sur les formules locales de l'indice
• Non-commutative Chern Characters of the C*-Algebras of spheres and quantum spheres