I'm learning about Kac-Moody algebras. The simplest example of an affine KM algebra that comes up is the Virasoro algebra, which is a central extension of the Witt algebra:
$$ [d_l, d_m] = (l-m) d_{l+m} + \frac{1}{12} (m^3 - m) \delta_{l+m,0} c $$
Is the Witt algebra (as above but without the central element $c$) in the KM classification, or any other classification of infinite dimensional Lie algebras? I'm pretty ignorant of the wider picture.