Valentin Ovsienko - Towards quantized complex numbers: $q$-deformed Gaussian integers and the Picard group

ocnmp:7480 - Open Communications in Nonlinear Mathematical Physics, July 29, 2021, Volume 1 - https://doi.org/10.46298/ocnmp.7480
Towards quantized complex numbers: $q$-deformed Gaussian integers and the Picard groupArticle

Authors: Valentin Ovsienko

    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.


    Volume: Volume 1
    Published on: July 29, 2021
    Accepted on: July 26, 2021
    Submitted on: May 14, 2021
    Keywords: Mathematics - Quantum Algebra,Mathematics - Combinatorics
    Funding:
      Source : OpenAIRE Graph
    • mathematical physics; Funder: French National Research Agency (ANR); Code: ANR-19-CE40-0021

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