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arXiv · 2002.03439

Nonstandard Quantum Complex Projective Line

Nicola Ciccoli·Albert Jeu-Liang Sheu
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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.

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Nicola Ciccoli, Albert Jeu-Liang Sheu. 2020-02-09. Nonstandard Quantum Complex Projective Line. https://doi.org/10.3842/sigma.2020.073

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