Normal forms for analytic Poisson structures

DOI10.2307/2007086zbMath0553.58004OpenAlexW2330800847MaRDI QIDQ802182

Jack F. Conn

Publication date: 1984

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2007086

zbMATH Keywords

Poisson manifoldLie algebra cohomologysplitting theoremPoisson tensorlinearization of Poisson structures

Mathematics Subject Classification ID

Differential forms in global analysis (58A10) Pseudogroups, differentiable groupoids and general structures on manifolds (58H99) Exterior differential systems (Cartan theory) (58A15) Cohomology of Lie (super)algebras (17B56)

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Nondegenerate Lie algebras ⋮ A new family of nondegenerate Lie algebras ⋮ LINEARIZATION OF POISSON–LIE STRUCTURES ON THE 2D EUCLIDEAN AND (1 + 1) POINCARÉ GROUPS ⋮ Normal forms of vector fields on Poisson manifolds ⋮ Linearization of some Poisson-Lie tensor ⋮ Rigidity of Poisson structures ⋮ Poisson geometry ⋮ On the Poisson geometry of the Adler-Gel'fand-Dikii brackets ⋮ A geometric approach to Conn's linearization theorem ⋮ Rigidity of Hamiltonian actions on Poisson manifolds ⋮ On Bott-Morse Foliations and their Poisson structures in dimension three ⋮ Nonlinearizability of the Iwasawa Poisson Lie structure ⋮ Normalisation holomorphe de structures de Poisson ⋮ Singularities and bifurcations of 3-dimensional Poisson structures ⋮ Linearization of Poisson brackets ⋮ Becchi–Rouet–Stora–Tyutin formalism and zero locus reduction ⋮ Deformation by quantization and rigidity of enveloping algebras. ⋮ Normal forms of Poisson structures ⋮ Nondegeneracy of the Lie algebra \(\text{aff}(n)\). ⋮ Classification analytique de structures de Poisson ⋮ Modèles locaux de structures de Poisson singulières en dimension 3 ⋮ Normal forms of Poisson structures with zero 1-jet at a point ⋮ A family of degenerate Lie algebras ⋮ Poisson cohomology in dimension two ⋮ Normal forms for locally exact Poisson structures in \(\mathbb R^3\)

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