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Symmetry, Integrability and Geometry: Methods and Applications, 2009, Volume 5, 063, 7 pp.
DOI: https://doi.org/10.3842/SIGMA.2009.063 (Mi sigma409) 		 
Non-Hamiltonian Actions and Lie-Algebra Cohomology of Vector Fields

Roberto Ferreiro Péreza, Jaime Muñoz Masquéb

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
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DOI: https://doi.org/10.3842/SIGMA.2009.063
Abstract: Two examples of $\mathrm{Diff}^+S^1$-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 $H^2(\mathfrak X(S^1))$.
Keywords: Gel'fand–Fuks cohomology; moment mapping; jet bundle.
Received: April 3, 2009; in final form June 8, 2009; Published online June 16, 2009
Bibliographic databases:
Document Type: Article
MSC: 58D15; 17B56; 22E65; 53D20; 53D30; 58A20
Language: English
Citation: Roberto Ferreiro Pérez, Jaime Muñoz Masqué, “Non-Hamiltonian Actions and Lie-Algebra Cohomology of Vector Fields”, SIGMA, 5 (2009), 063, 7 pp.
Citation in format AMSBIB
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