2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77174By introducing a result that guarantees a given bialgebra to be a Hopf algebra under a natural condition, we show that the quantum automorphism group of the algebra k[x] of polynomials over a field k (of any characteristic) is the universal quantum a x + b group, generalizing the fact that the automorphism group of k[x] is the a x + b group. The q-deformation of the a x + b group is then seen as one among a certain family ${\mathcal A}_{q, n}$ of quantum subgroups of this universal quantum group.AMSLATEX, 9 papgesOperator AlgebrasQuantum Algebratext