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

Jaime Mu\~noz Masqu\'e; Roberto Ferreiro P\'erez

arxiv: 0906.2988 · v1 · submitted 2009-06-16 · 🧮 math.DG · math-ph· math.MP

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

Roberto Ferreiro P\'erez , Jaime Mu\~noz Masqu\'e This is my paper

classification 🧮 math.DG math-phmath.MP

keywords cohomologyactionsadmitalgebrabundlesclassclosedcohomological

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

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