2017/05/12 by Albert Jeu-Liang Sheu, Sheu, Albert Jeu-Liang
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.1705.04611
openalex publication_date 2017/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We work on the classification of isomorphism classes of finitely generated projective modules over the C*-algebras C( ℙn( T) ) and C( \mathbbSH2n+1) of the quantum complex projective spaces ℙn( T ) and the quantum spheres \mathbbSH2n+1, and the quantum line bundles Lk over ℙn( T) , studied by Hajac and collaborators. Motivated by the groupoid approach of Curto, Muhly, and Renault to the study of C*-algebraic structure, we analyze C( ℙn( T) ) , C( \mathbbSH2n+1) , and Lk in the context of groupoid C*-algebras, and then apply Rieffel's stable rank results to show that all finitely generated projective modules over C( \mathbbSH 2n+1) of rank higher than \lfloor (n)/(2)\rfloor +3 are free modules. Furthermore, besides identifying a large portion of the positive cone of the K0-group of C( ℙn( T) ) , we also explicitly identify Lk with concrete representative elementary projections over C( ℙ n( T) ) .