Extensions of representations of Lie algebras (Q1098920)

Let \(f: L_ 1\to L_ 2\) be a homomorphism of finite-dimensional Lie algebras over a field of characteristic zero. Let V be a finite- dimensional \(L_ 1\)-module. The author investigates when V embeds as a sub \(L_ 1\)-module of a finite-dimensional \(L_ 2\)-module. One can assume f injective, in which case the author gives conditions which are necessary and sufficient, provided that either \(f(Radical L_ 1)\subset Radical L_ 2\) or \(L_ 1=[L_ 1,L_ 1]\). The methods of proof make heavy use of the Hopf algebra structure on the representative functions on a Lie algebra.