Non-Hamiltonian actions and Lie-algebra cohomology of vector fields

DOI10.3842/SIGMA.2009.063zbMATH Open1190.58013arXiv0906.2988OpenAlexW1994692526WikidataQ115219702 ScholiaQ115219702MaRDI QIDQ970243

Jaime Muñoz Masqué, R. Ferreiro Pérez

Publication date: 17 May 2010

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

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 $H^2(mathfrakX(S^1))$.

Full work available at URL: https://arxiv.org/abs/0906.2988

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zbMATH Keywords

moment mappingjet bundleGel'fand-fuks cohomology

Mathematics Subject Classification ID

Jets in global analysis (58A20) Infinite-dimensional Lie groups and their Lie algebras: general properties (22E65) Momentum maps; symplectic reduction (53D20) Cohomology of Lie (super)algebras (17B56) Symplectic structures of moduli spaces (53D30) Manifolds of mappings (58D15)

Related Items (4)

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