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Infinitesimal Modular Group: $q$-Deformed $\mathfrak{sl}_2$ and Witt Algebra (2308.06158v4)
Published 11 Aug 2023 in math.QA, math-ph, and math.MP
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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