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Deformations of vector fields and Hamiltonian vector fields on the plane

Authors: Nico van den Hijligenberg, Youri Kotchetkov and Gerhard Post
Journal: Math. Comp. 64 (1995), 1215-1226
MSC: Primary 17B66; Secondary 17B56
MathSciNet review: 1297480
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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))$.

References [Enhancements On Off] (What's this?)

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Keywords: Lie algebras, deformations
Article copyright: © Copyright 1995 American Mathematical Society

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