  We demonstrate that the gauge-fixed Lagrangian of the Christ-Lee model
respects four fermionic symmetries, namely; (anti-)BRST symmetries,
(anti-)co-BRST symmetries within the framework of BRST formalism. The
appropriate anticommutators amongst the fermionic symmetries lead to a unique
bosonic symmetry. It turns out that the algebra obeyed by the symmetry
transformations (and their corresponding conserved charges) is reminiscent of
the algebra satisfied by the de Rham cohomological operators of differential
geometry. We also provide the physical realizations of the cohomological
operators in terms of the symmetry properties. Thus, the present model provides
a simple model for the Hodge theory.
