The Schouten bracket and Hamiltonian operators

DOI10.1007/BF01086188zbMath0455.58013OpenAlexW2094292604MaRDI QIDQ1150196

I. Ya. Dorfman, Israel M. Gel'fand

Publication date: 1981

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01086188

zbMATH Keywords

Hamiltonian pairsHamiltonian operatorsSchouten bracketformal variational calculusNijenhuis bracketHamiltonian structure of the Lax equationLie algebra of vector fields on a manifold

Mathematics Subject Classification ID

Related Items (26)

Hamiltonian differencing of fluid dynamics ⋮ Novikov Super-Algebras with Associative Non-Degenerate Super-Symmetric Bilinear Forms ⋮ Block-diagonalizability problem for hydrodynamic type systems ⋮ Lax–Nijenhuis operators for integrable systems ⋮ R-matrices and higher Poisson brackets for integrable systems ⋮ Theory of tensor invariants of integrable Hamiltonian systems. I: Incompatible Poisson structures ⋮ Decoupling problem for systems of quasi-linear PDE's ⋮ Geometry of jet spaces and integrable systems ⋮ Algebraic identities for the Nijenhuis tensors ⋮ New integrable differential-difference and fractional nonlinear dynamical systems and their algebro-analytical properties ⋮ A note on Hamiltonian structure ⋮ Hamiltonian Dynamics of a spaceship in Alcubierre and G\"odel metrics: Recursion operators and underlying master symmetries ⋮ Courant-like brackets and loop spaces ⋮ WDVV equations and invariant bi-Hamiltonian formalism ⋮ Hamiltonian formalism of Whitham-type hierarchies and topological Landau- Ginsburg models ⋮ Linear bundles of Lie algebras and their applications ⋮ Algebraic identity for the Schouten tensor and bi-Hamiltonian systems ⋮ R structures, Yang–Baxter equations, and related involution theorems ⋮ ``Universal Lie algebra extensions and their Casimir invariants via commutative structures ⋮ Novikov superalgebras with A 0 = A 1 A 1 ⋮ Noncommutative Kepler dynamics: symmetry groups and bi-Hamiltonian structures ⋮ Super Hamiltonian operators and Lie superalgebras ⋮ Induction of Hamiltonian Poisson actions ⋮ Differential geometry of the vortex filament equation ⋮ On the simplectization of bi-Hamiltonian structures ⋮ Poisson geometry of the filament equation

Cites Work

• Unnamed Item

This page was built for publication: The Schouten bracket and Hamiltonian operators