DEFORMATIONS OF VECTOR-FIELDS AND HAMILTONIAN VECTOR-FIELDS ON THE PLANE

For the Lie algebras L(1)(H(2)) and LI(W(2)),we study their infinitesi mal deformations and the corresponding global ones. We show that, as i n the case of L(1)(W(1)),each integrable ihfinitesimal deformation of L(1)(H(2)) and L(1)(W(2)) can be represented by a 2-cocycle that defin es a global deformation by means of a trivial extension. We also illus trate that all deformations of L(1)(H(2)) arise as restrictions of def ormations of L(1)(W(2)).