Schlichenmaier Martin gl(infinity) ,diff_A S:2, diff_A T:2 and su(N)- Approximation (40K, amstex 1.1) ABSTRACT. A scheme for the approximation of infinite dimensional Lie algebras by a series of finite dimensional ones is given. For the algebras diff_A S:2, diff_A T:2 and related Lie algebras this scheme is applied. (This is a write-up of a talk)