DEFORMATIONS OF VECTOR FIELDS AND HAMILTONIAN VECTOR FIELDS ON THE PLANE

摘要

For the Lie algebras L(1)(H(2)) and LI(W(2)),we study their infinitesimal deformations and the corresponding global ones. We show that, as in 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 defines a global deformation by means of a trivial extension. We also illustrate that all deformations of L(1)(H(2)) arise as restrictions of deformations of L(1)(W(2)). [References: 6]