Nonstandard Quantum Complex Projective Line
Operator Algebras
2020-08-04 v3 Quantum Algebra
Abstract
In our attempt to explore how the quantum nonstandard complex projective spaces 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 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 being a concrete weighted double shift.
Cite
@article{arxiv.2002.03439,
title = {Nonstandard Quantum Complex Projective Line},
author = {Nicola Ciccoli and Albert Jeu-Liang Sheu},
journal= {arXiv preprint arXiv:2002.03439},
year = {2020}
}