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arXiv · 2308.06158

Infinitesimal Modular Group: $q$-Deformed $\mathfrak{sl}_2$ and Witt Algebra

Alexander Thomas
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Abstract

We describe new $q$-deformations of the 3-dimensional Heisenberg algebra, the simple Lie algebra $\mathfrak{sl}_2$ and the Witt algebra. They are constructed through a realization as differential operators. These operators are related to the modular group and $q$-deformed rational numbers defined by Morier-Genoud and Ovsienko and lead to $q$-deformed M\"obius transformations acting on the hyperbolic plane.

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BibTeXRIS

Alexander Thomas. 2023-08-11. Infinitesimal Modular Group: $q$-Deformed $\mathfrak{sl}_2$ and Witt Algebra. https://doi.org/10.3842/sigma.2024.053

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