Infinitesimal Modular Group: -Deformed ₂ and Witt Algebra - Thomas, Alexander (Symmetry, Integrability and Geometry: Methods and Applications, 2024)
We describe new -deformations of the 3-dimensional Heisenberg algebra, the simple Lie algebra ₂, and the Witt algebra. They are constructed through a realization as differential operators. These operators are related to the modular group and -deformed rational numbers defined by Morier-Genoud and Ovsienko and lead to -deformed Möbius transformations acting on the hyperbolic plane.