  In this article, we revisit some aspects of the computation of the cohomology
class of $H^2 ( \text{Witt}, \mathbb{C})$ using some methods in two-dimensional
conformal field theory and conformal algebra to obtain the one-dimensional
central extension of the Witt algebra to the Virasoro algebra. Even though this
is well-known in the context of standard mathematical physics literature, the
operator product expansion of the energy-momentum tensor in two-dimensional
conformal field theory is presented almost axiomatically. In this paper, we
attempt to reformulate it with the help of a suitable modification of conformal
algebra (as developed by V. Kac), and apply it to compute the representative
element of the cohomology class which gives the desired central extension. This
paper was written in the scope of an undergraduate's exploration of conformal
field theory and his attempt to gain insight on the subject from a mathematical
perspective.
