Quantum teardrops

Abstract

Algebras of functions on quantum weighted projective spaces are introduced, and the structure of quantum weighted projective lines or quantum teardrops are described in detail. In particular the presentation of the coordinate algebra of the quantum teardrop in terms of generators and relations and classification of irreducible *-representations are derived. The algebras are then analysed from the point of view of Hopf-Galois theory or the theory of quantum principal bundles. Fredholm modules and associated traces are constructed. C*-algebras of continuous functions on quantum weighted projective lines are described and their K-groups computed.

18 pages

Cited by in corpus (13)

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• Complex geometry of quantum cones
• Circle actions on a quantum Seifert manifold
• The geometry of quantum lens spaces: real spectral triples and bundle structure
• Notes on quantum weighted projective spaces and multidimensional teardrops
• Non-surjective pullbacks of graph C*-algebras from non-injective pushouts of graphs
• The Structure of Line Bundles over Quantum Teardrops
• Weighted circle actions on the Heegaard quantum sphere
• On Noncommutative Geometry of Orbifolds
• Projective Modules over Quantum Projective Line
• Piecewise Principal Coactions of Co-Commutative Hopf Algebras
• Morita Equivalence and Spectral Triples on Noncommutative Orbifolds
• Gysin exact sequences for quantum weighted lens spaces