  We calculate Ext^*_{SL_2(k)}(\Delta(\lambda), \Delta(\mu)),
Ext^*_{SL_2(k)}(L(\lambda), \Delta(\mu)), Ext^*_{SL_2(k)}(\Delta(\lambda),
L(\mu)), and Ext^*_{SL_2(k)}(L(\lambda), L(\mu)), where \Delta(\lambda) is the
Weyl module of highest weight \lambda, L(\lambda) is the simple SL_2(k)-module
of highest weight \lambda and our field k is algebraically closed of positive
characteristic. We also get analogous results for the Dipper-Donkin
quantisation. To do thus we construct the Lyndon-Hochschild-Serre spectral
sequence in a new way, and find a new condition for the E_2 page of any
spectral sequence to be the same as the E_\infty page.
