Geodesic
Non-Hamiltonian Actions and Lie-Algebra Cohomology of Vector Fields
Symmetry, integrability and geometry: methods and applications, Tome 5 (2009) Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{SIGMA_2009_5_a62,
     author = {Roberto Ferreiro P\'erez and Jaime Mu\~noz Masqu\'e},
     title = {Non-Hamiltonian {Actions} and {Lie-Algebra} {Cohomology} of {Vector} {Fields}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2009},
     volume = {5},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2009_5_a62/}
}
TY  - JOUR
AU  - Roberto Ferreiro Pérez
AU  - Jaime Muñoz Masqué
TI  - Non-Hamiltonian Actions and Lie-Algebra Cohomology of Vector Fields
JO  - Symmetry, integrability and geometry: methods and applications
PY  - 2009
VL  - 5
UR  - http://geodesic.mathdoc.fr/item/SIGMA_2009_5_a62/
LA  - en
ID  - SIGMA_2009_5_a62
ER  - 
%0 Journal Article
%A Roberto Ferreiro Pérez
%A Jaime Muñoz Masqué
%T Non-Hamiltonian Actions and Lie-Algebra Cohomology of Vector Fields
%J Symmetry, integrability and geometry: methods and applications
%D 2009
%V 5
%U http://geodesic.mathdoc.fr/item/SIGMA_2009_5_a62/
%G en
%F SIGMA_2009_5_a62
Roberto Ferreiro Pérez; Jaime Muñoz Masqué. Non-Hamiltonian Actions and Lie-Algebra Cohomology of Vector Fields. Symmetry, integrability and geometry: methods and applications, Tome 5 (2009). http://geodesic.mathdoc.fr/item/SIGMA_2009_5_a62/

[1] Ferreiro Pérez R., “Equivariant characteristic forms in the bundle of connections”, J. Geom. Phys., 54 (2005), 197–212 ; math-ph/0307022 | DOI | MR | Zbl

[2] Ferreiro Pérez R., “Local cohomology and the variational bicomplex”, Int. J. Geom. Methods Mod. Phys., 5 (2008), 587–604 | DOI | MR | Zbl

[3] Ferreiro Pérez R., Muñoz Masqué J., Pontryagin forms on $(4k-2)$-manifolds and symplectic structures on the spaces of Riemannian metrics, math.DG/0507076

[4] Fuks D. B., Cohomology of infinite-dimensional Lie algebras, Contemporary Soviet Mathematics, Consultants Bureau, New York, 1986 | MR

[5] Gel'fand I. M., Fuks D. B., “Cohomologies of the Lie algebra of vector fields on the circle”, Funkcional. Anal. i Prilozen., 2:4 (1968), 92–93 | MR

[6] Hamilton R., “The inverse function theorem of Nash and Moser”, Bull. Amer. Math. Soc. (N.S.), 7 (1982), 65–222 | DOI | MR | Zbl

[7] McDuff D., Salamon D., Introduction to symplectic topology, Oxford Mathematical Monographs, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1995 | MR | Zbl

[8] Pohjanpelto J., Anderson I. M., “Infinite-dimensional Lie algebra cohomology and the cohomology of invariant Euler–Lagrange complexes: a preliminary report”, Differential Geometry and Applications (Brno, 1995), Masaryk Univ., Brno, 1996, 427–448 | MR | Zbl