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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 

 

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
DOI: https://doi.org/10.1090/S0025-5718-1995-1297480-5
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))$.


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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1995-1297480-5
Keywords: Lie algebras, deformations
Article copyright: © Copyright 1995 American Mathematical Society