  We find that Siegel type chiral boson with a parameter-dependent Lorentz
non-covariant masslike term for the gauge fields to be equivalent to the chiral
Schwinger model with one parameter class of Faddeevian anomaly if the model is
described in terms of Floreanini-Jackiw type chiral boson. By invoking the
Wess-Zunino field gauge-invariant reformulation is made. It has been shown that
the gauge-invariant model has the same physical content as its gauge
non-invariant ancestor had. The BRST invariant effective action corresponding
to this model has also been constructed. All the nilpotent symmetries
associated with the BRST symmetry along with the bosonic, ghost, and discrete
symmetries have been systematically studied. We establish that the nilpotent
charges corresponding to these symmetries resemble the algebra of the de Rham
cohomological operators in differential geometry. In the environment of
conserved charges associated with the models, we study the Hodge decomposition
theorem on the compact manifold.
