Non-Hamiltonian Actions and Lie-Algebra Cohomology of Vector Fields

Mathematics – Differential Geometry

Scientific paper

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Scientific paper

10.3842/SIGMA.2009.063

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
$H^2(\mathfrak{X}(S^1))$.

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