Nonstandard Quantum Complex Projective Line
In our attempt to explore how the quantum nonstandard complex projective spaces ℂⁿq,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 esta...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2020 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2020
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210775 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Nonstandard Quantum Complex Projective Line. Nicola Ciccoli and Albert Jeu-Liang Sheu. SIGMA 16 (2020), 073, 14 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | In our attempt to explore how the quantum nonstandard complex projective spaces ℂⁿq,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 (ℂ¹q,c) with the pull-back of two copies of the Toeplitz *-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 (ℂ¹q,c) being a concrete weighted double shift.
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| ISSN: | 1815-0659 |