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SIGMA 5 (2009), 063, 7 pages arXiv:0906.2988
https://doi.org/10.3842/SIGMA.2009.063
Contribution to the Special Issue “Élie Cartan and Differential Geometry”
Non-Hamiltonian Actions and Lie-Algebra Cohomology of Vector Fields
Roberto Ferreiro Pérez a and Jaime Muñoz Masqué b
a) Departamento de Economía Financiera
y Contabilidad I, Facultad de Ciencias Económicas y Empresariales, UCM, Campus de Somosaguas, 28223-Pozuelo de Alarcón, Spain
b) Instituto de Física Aplicada, CSIC, C/ Serrano 144, 28006-Madrid, Spain
Received April 03, 2009, in final form June 08, 2009; Published online June 16, 2009
Abstract
Two examples of Diff+S1-invariant closed
two-forms obtained from forms on jet bundles, which does not admit
equivariant moment maps are presented. The corresponding
cohomological obstruction is computed and shown to coincide with a
nontrivial Lie algebra cohomology class on
H2(X(S1)).
Key words:
Gel'fand-Fuks cohomology; moment mapping; jet bundle.
pdf (200 kb)
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