  The extension structure of the 2-dimensional current algebra of non-linear
sigma models is analysed by introducing Kostant Sternberg $(L,M)$ systems. It
is found that the algebra obeys a two step extension by abelian ideals. The
second step is a non-split extension of a representation of the quotient of the
algebra by the first step of the extension. The cocycle which appears is
analysed.
