Nonstandard Quantum Complex Projective Line

Symmetry Integrability and Geometry-Methods and Applications

article

Nicola Ciccoli¹  Albert Jeu-Liang Sheu² 

[1] Dipartimento di Matematica e Informatica, University of Perugia;Department of Mathematics, University of Kansas

关键词: quantum homogeneous space;    Toeplitz algebra;    weighted shi;   

DOI  :  10.3842/SIGMA.2020.073

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown