Differential Operators on the Projective Line

In this video, we look at the ring of differential operators on the complex projective line. The idea is to consider the natural action of the algebraic group SL_2(C) on the projective line, which gives an action of the universal enveloping algebra U(sl_2(C)) as differential operators on the projective line. We study the resulting homomorphism between this universal enveloping algebra and the ring of differential operators which gives a close relationship between the two.