We present a novel approach to the polaron problem developed on the notion of quantum groups, also known as q-deformed Lie algebras. In this approach, the presence of an impurity in a bath can be depicted as a deformation of the Lie algebra of the bosonic creation and annihilation operators of the bath. In particular, we introduce a simple q-deformed bosonic Hamiltonian whose truncation on the quartic level in the usual bosonic creation and annihilation operators corresponds to the Fröhlich-Bogoliubov polaron Hamiltonian. By using the q-deformed Lie algebra, the introduced parent Hamiltonian allows us to derive the ground state energy of the Fröhlich-Bogoliubov Hamiltonian analytically for the regime where the Bogoliubov dispersion law takes the phonon-like form