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Nonstandard Quantum Complex Projective Line (2002.03439v3)
Published 9 Feb 2020 in math.OA and math.QA
Abstract: In our attempt to explore how the quantum nonstandard complex projective spaces $\mathbb{C}P_{q,c}{n}$ 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\big(\mathbb{C}P_{q,c}{1}\big) $ 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 non-obvious details, such as a prominent generator of $C\big(\mathbb{C}P_{q,c}{1}\big) $ being a concrete weighted double shift.