  The importance of polarised gluons fragmenting into $\Lambda$ in the
polarised $e^+ e^-$ annihilation is discussed using the Altarelli-Parisi
evolution equations satisfied by the quark and gluon fragmentation functions.
In this context, the polarised fragmentaion function $\hat g_1^\Lambda(x,Q^2)$
appearing in the cross section is discussed within the parton model. We relate
this fragmentation function to the quark, anti-quark and gluon fragmentation
functions and also find the QCD corrections to order $\alpha_s$.
