Valentin Ovsienko
2021.3.18Open Communications in Nonlinear Mathematical Physics
tlooto Summary
First step towards a theory of q-deformed complex numbers, proving existence and uniqueness of operator compatible with modular group action.
Abstract
This work is a first step towards a theory of "$q$-deformed complex numbers". Assuming the invariance of the $q$-deformation under the action of the modular group I prove the existence and uniqueness of the operator of translations by~$i$ compatible with this action. Obtained in such a way $q$-deformed Gaussian integers have interesting properties and are related to the Chebyshev polynomials.
Comment: 21 pages
Citation format
OVSIENKO, Valentin. Towards quantized complex numbers: $Q$-deformed gaussian integers and the picard group [preprint]. arXiv, 2021. arXiv:2103.10800.