Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 5 (2009), 063, 7 pages      arXiv:0906.2988
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

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.

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