We work on the classification of isomorphism classes of finitely generated projective modules over the C*-algebras and of the quantum complex projective spaces and the quantum spheres , and the quantum line bundles over , studied by Hajac and collaborators. Motivated by the groupoid approach of Curto, Muhly, and Renault to the study of C*-algebraic structure, we analyze , , and in the context of groupoid C*-algebras, and then apply Rieffel's stable rank results to show that all finitely generated projective modules over of rank higher than are free modules. Furthermore, besides identifying a large portion of the positive cone of the -group of , we also explicitly identify with concrete representative elementary projections over .
Cite this article
Albert Jeu-Liang Sheu, Vector bundles over multipullback quantum complex projective spaces. J. Noncommut. Geom. 15 (2021), no. 1, pp. 305–345DOI 10.4171/JNCG/401