  The notion of defining relations is well-defined for any nilpotent Lie
algebra. Therefore a conventional way to present a simple Lie algebra G is by
splitting it into the direct sum of a commutative Cartan subalgebra and two
maximal nilpotent subalgebras (positive and negative) and together the
generators of both these nilpotent subalgebras together generate G. Though
there are many relations between these generators, they are neat (Serre
relations).
  It is possible to determine the relations for generators of different type,
e.g, with the principal embeddings of sl(2) into G one can associate only TWO
elements that generate G. We explicitly describe the corresponding
presentations of simple Lie algebras, for all finite dimensional and certain
infinite dimensional ones; namely, for the Lie algebra "of matrices of a
complex size" realized as a subalgebra of the Lie algebra of differential
operators in 1 indeterminate. The relations obtained are rather simple.
  Our results might be of interest in applications to integrable systems (like
vector-valued Liouville (or Leznov-Saveliev, or 2-dimensional Toda) equations
and KdV-type equations). They also indicate how to q-quantize the Lie algebra
of matrices of complex size.
