2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/153754Is is shown that the quantum Weyl group of $sl_2$ contains an element that is a cylinder twist, i.e. it gives rise to representations of the braid group of Coxeter type B.Quantum AlgebraThe Cylinder braiding of the quantum Weyl group of $sl_2$text