Consider the Lie algebras $L_{r,t}^{s}:[ K_{1},K_{2}] = sK_{3}$ , $[K_{3},K_{1}] = rK_{1}$ , $[K_{3},K_{2}] = -rK_{2}$ , $[K_{3},K_{4}] = 0$ , $[K_{4},K_{1}] = -tK_{1}$ , and $[K_{4},K_{2}] = tK_{2}$ , subject to the physical conditions, $K_3$ and $K_4$ are real diagonal operators representing energy, $K_2 = K_{1}^{\dagger}$ , and the Hamiltonian $H =\omega_{1}K_{3} + (\omega_{1}+\omega_{2})K_{4} +\lambda(t)(K_{1}e^{-i\phi}+K_{2}e^{i\phi})$ is a Hermitian operator. Matrix representations are discussed and faithful representations of least degree for $L_{r,t}^{s}$ satisfying the physical requirements are given for appropriate values of $r,s,t\in\mathbb{R}$ .