Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 10 (2014), 027, 11 pages      arXiv:1403.5626      https://doi.org/10.3842/SIGMA.2014.027
Contribution to the Special Issue on Noncommutative Geometry and Quantum Groups in honor of Marc A. Rieffel

The Structure of Line Bundles over Quantum Teardrops

Albert Jeu-Liang Sheu
Department of Mathematics, University of Kansas, Lawrence, KS 66045, USA

Received October 07, 2013, in final form March 15, 2014; Published online March 22, 2014

Abstract
Over the quantum weighted 1-dimensional complex projective spaces, called quantum teardrops, the quantum line bundles associated with the quantum principal U(1)-bundles introduced and studied by Brzezinski and Fairfax are explicitly identified among the finitely generated projective modules which are classified up to isomorphism. The quantum lens space in which these quantum line bundles are embedded is realized as a concrete groupoid C*-algebra.

Key words: quantum line bundle; quantum principal bundle; quantum teardrop; quantum lens space; groupoid C*-algebra; finitely generated projective module; quantum group.

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