  Dynamical symmetry algebra for a semiconfined harmonic oscillator model with
a position-dependent effective mass is constructed. Selecting the starting
point as a well-known factorization method of the Hamiltonian under
consideration, we have found three basis elements of this algebra. The algebra
defined through those basis elements is a $\mathfrak{su}\left(1,1 \right)$
Heisenberg-Lie algebra. Different special cases and the limit relations from
the basis elements to the Heisenberg-Weyl algebra of the non-relativistic
quantum harmonic oscillator are discussed, too.
