2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/187154In this paper we consider Hamiltonian systems on the quantum plane and we show that the set of Q-meromorphic Hamiltonians is a Virasoro algebra with central charge zero and the set of Hamiltonian derivations of the algebra of $Q$-analytic functions ${\cal A}_q$ with values in the algebra of $Q$-meromorphic functions ${\cal M}_q$ is the Lie algebra $sl(2,A_1(q)).$ Moreover we will show that any motion on a quantum space is associated with a quadratic Hamiltonian.18 pages, LaTeX, no figuresHigh Energy Physics - Theorytext