  Whenever the group $\R^n$ acts on an algebra $\calA$, there is a method to
twist $\cal A$ to a new algebra $\calA_\theta$ which depends on an
antisymmetric matrix $\theta$ ($\theta^{\mu \nu}=-\theta^{\nu
\mu}=\mathrm{constant}$). The Groenewold-Moyal plane $\calA_\theta(\R^{d+1})$
is an example of such a twisted algebra. We give a general construction to
realise this twist in terms of $\calA$ itself and certain ``charge'' operators
$Q_\mu$. For $\calA_\theta(\R^{d+1})$, $Q_\mu$ are translation generators. This
construction is then applied to twist the oscillators realising the Kac-Moody
(KM) algebra as well as the KM currents. They give different deformations of
the KM algebra. From one of the deformations of the KM algebra, we construct,
via the Sugawara construction, the Virasoro algebra. These deformations have
implication for statistics as well.
