Infinitesimal Modular Group: $q$-Deformed $\mathfrak{sl}_2$ and Witt Algebra
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Published:2024-06-20
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ISSN:1815-0659
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Container-title:Symmetry, Integrability and Geometry: Methods and Applications
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Short-container-title:SIGMA
Author:
,Thomas Alexander, ,
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 Möbius transformations acting on the hyperbolic plane.
Publisher
SIGMA (Symmetry, Integrability and Geometry: Methods and Application)