Infinitesimal Modular Group: $q$-Deformed $\mathfrak{sl}_2$ and Witt Algebra
Quantum Algebra
2024-06-21 v4 Mathematical Physics
math.MP
Abstract
We describe new -deformations of the 3-dimensional Heisenberg algebra, the simple Lie algebra 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 M\"obius transformations acting on the hyperbolic plane.
Keywords
Cite
@article{arxiv.2308.06158,
title = {Infinitesimal Modular Group: $q$-Deformed $\mathfrak{sl}_2$ and Witt Algebra},
author = {Alexander Thomas},
journal= {arXiv preprint arXiv:2308.06158},
year = {2024}
}