Deformations of vector fields and Hamiltonian vector fields on the plane

van den Hijligenberg, Nico; Kotchetkov, Youri; Post, Gerhard

doi:10.1090/S0025-5718-1995-1297480-5

Deformations of vector fields and Hamiltonian vector fields on the plane
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by Nico van den Hijligenberg, Youri Kotchetkov and Gerhard Post PDF

Math. Comp. 64 (1995), 1215-1226 Request permission

Abstract:

For the Lie algebras ${L_1}(H(2))$ and ${L_1}(W(2))$, we study their infinitesimal deformations and the corresponding global ones. We show that, as in the case of ${L_1}(W(1))$, each integrable infinitesimal 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 ${L_1}(W(2))$.

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Cohomology of infinite-dimensional Lie algebras