  The algebraic approach to the spectrum of quasinormal modes has been made as
simple as possible for the BTZ black hole by the strategy developed in
\cite{Zhang}. By working with the self-dual warped AdS black hole, we
demonstrate in an explicit way that such a strategy can be well adapted to
those warped AdS balck holes with the $SL(2,R)\times U(1)$ isometry. To this
end, we first introduce two associated tensor fields with the quadratic Casimir
of $SL(2,R)\times U(1)$ Lie algebra in the self-dual warped AdS black hole and
show that they correspond essentially to the metric and volume element up to a
constant prefactor, respectively. Then without appealing to any concrete
coordinate system, we can further show that the solutions to the equations of
motion for the scalar, vector, spinor fields all fall into the representations
of the $SL(2,R)\times U(1)$ Lie algebra by a purely abstract tensor and spinor
analysis. Accordingly, the corresponding spectrum of quasinormal modes for each
fixed azimuthal quantum number can be derived algebraically as the infinite
tower of descendants of the highest weight mode of the $SL(2,R)$ Lie
subalgebra.
