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Projective Modules Over Quantum Projective Line

Albert Jeu-Liang Sheu

Department of Mathematics, University of Kansas, Lawrence, KS 66045, USA

https://doi.org/10.1142/S0129167X17500227Cited by:1 (Source: Crossref)

Abstract

Taking a groupoid C*-algebra approach to the study of the quantum complex projective spaces $ℙ^{n} (𝒯)$ constructed from the multipullback quantum spheres introduced by Hajac and collaborators, we analyze the structure of the C*-algebra $C (ℙ^{1} (𝒯))$ realized as a concrete groupoid C*-algebra, and find its $K$ -groups. Furthermore, after a complete classification of the unitary equivalence classes of projections or equivalently the isomorphism classes of finitely generated projective modules over the C*-algebra $C (ℙ^{1} (𝒯))$ , we identify those quantum principal $U (1)$ -bundles introduced by Hajac and collaborators among the projections classified.

Keywords:

AMSC: 46L80, 46L85

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