ON THE UNIVERSAL ENVELOPING ALGEBRA OF SL2(C)

For the universal enveloping algebra U of sl2(C), we consider the decomposition U congruent-to Z X H. Here Z is the center of U, generated by the (unique) Casimir operator DELTA, and H is the sl2-module pi0 + pi1 + pi2..., where pi(k) is the irreducible representation of sl2 with dimension 2k + 1. We choose a basis in U according to this decomposition and we study the Lie algebra structure of U over the ring Z.