Boris Kruglikov.
  "Symplectic and contact Lie algebras with an application to
  Monge-Ampere equations".

  Proceedings of Steklov Mathematical Institute, v.221, 232--246 (1998).

We study symplectic and contact Lie algebras from geometric point of
view. We define contactization and symplectization procedures and
describe its main properties. We give classification
of such algebras in dimensions 3 and 4. The classification in
dimension~4 is closely connected with normal forms of nondegenerate
elliptic equations of the second order on two-dimensional surfaces
with transitive symmetry group in first jets. We point out this
connection and discuss normal forms.