Projective Modules over Quantum Projective Line

Abstract

Taking a groupoid C*-algebra approach to the study of the quantum complex projective spaces ${\mathbb{P}}^n\left(\mathcal{T}\right)$ constructed from the multipullback quantum spheres introduced by Hajac and collaborators, we analyze the structure of the C*-algebra $C\left({\mathbb{P}}^1\left(\mathcal{T}\right)\right)$ 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 $C\left({\mathbb{P}}^1\left(\mathcal{T}\right)\right)$, we identify those quantum principal $U\left(1\right)$-bundles introduced by Hajac and collaborators among the projections classified.

References in corpus (2)

• The Structure of Line Bundles over Quantum Teardrops
• Finitely-Generated Projective Modules over the Theta-deformed 4-sphere