Key points are not available for this paper at this time.
We describe new q-deformations of the 3-dimensional Heisenberg algebra, the simple Lie algebra sl₂ 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.
Alexander Thomas (Thu,) studied this question.