Search results for "Schouten–Nijenhuis bracket"

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The Schouten - Nijenhuis bracket, cohomology and generalized Poisson structures

1996

Newly introduced generalized Poisson structures based on suitable skew-symmetric contravariant tensors of even order are discussed in terms of the Schouten-Nijenhuis bracket. The associated `Jacobi identities' are expressed as conditions on these tensors, the cohomological contents of which is given. In particular, we determine the linear generalized Poisson structures which can be constructed on the dual spaces of simple Lie algebras.

High Energy Physics - TheoryMathematics - Differential GeometryPhysicsPure mathematicsSchouten–Nijenhuis bracketFOS: Physical sciencesGeneral Physics and AstronomyOrder (ring theory)Statistical and Nonlinear PhysicsPoisson distributionCohomologysymbols.namesakeBracket (mathematics)High Energy Physics - Theory (hep-th)Differential Geometry (math.DG)Simple (abstract algebra)Mathematics - Quantum AlgebraLie algebraFOS: MathematicssymbolsCovariance and contravariance of vectorsQuantum Algebra (math.QA)Mathematics::Symplectic GeometryMathematical PhysicsJournal of Physics A: Mathematical and General
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Poisson-Nijenhuis structures and the Vinogradov bracket

1994

We express the compatibility conditions that a Poisson bivector and a Nijenhuis tensor must fulfil in order to be a Poisson-Nijenhuis structure by means of a graded Lie bracket. This bracket is a generalization of Schouten and Frolicher-Nijenhuis graded Lie brackets defined on multivector fields and on vector valued differential forms respectively.

Schouten–Nijenhuis bracketGraded Lie algebraAlgebraFrölicher–Nijenhuis bracketPoisson bracketAdjoint representation of a Lie algebraNonlinear Sciences::Exactly Solvable and Integrable SystemsMathematics::Quantum AlgebraPoisson manifoldLie bracket of vector fieldsLie derivativeMathematics::Differential GeometryGeometry and TopologyMathematics::Symplectic GeometryAnalysisMathematicsAnnals of Global Analysis and Geometry
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