Nonstandard Quantum Complex Projective Lin

Abstract

In our attempt to explore how the quantum nonstandard complex projective spaces CP n q,c studied by Korogodsky, Vaksman, Dijkhuizen, and Noumi are related to those arising from the geometrically constructed Bohr-Sommerfeld groupoids by Bonechi, Ciccoli, Qiu, Staffolani, and Tarlini, we were led to establish the known identification of C CP 1 q,c with the pull-back of two copies of the Toeplitz C *-algebra along the symbol map in a more direct way via an operator theoretic analysis, which also provides some interesting nonobvious details, such as a prominent generator of C CP 1 q,c being a concrete weighted double shift.