Symmetry Integrability and Geometry-Methods and Applications | |
Nonstandard Quantum Complex Projective Line | |
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
【 预 览 】
Files | Size | Format | View |
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RO202106300000653ZK.pdf | 369KB | download |