2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/54371We discuss the $q$-Virasoro algebra based on the arguments of the Noether currents in a two-dimensional massless fermion theory as well as in a three-dimensional nonrelativistic one. Some notes on the $q$-differential operator realization and the central extension are also included.revised and extended version of HUPD-9201, a wrong statement of HUPD-9204 is corrected, to be published in Z. Phys. CHigh Energy Physics - Theorytext